HWI_NDVI_parks_Appendix
Yan Lam Grace, Lou
2024-04-19
Overview
In this study, we will be modelling the monthly mean Normalized Difference Vegetation Index (NDVI) of 25 selected Canadian national parks over 22 years with the frequency of HWIs in each park over 12 years to identify trends.
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## as.Date, as.Date.numericlibrary(canadianmaps) #import annotated map of Canada
library(sf) # spatial data## Warning: package 'sf' was built under R version 4.3.3## Linking to GEOS 3.11.2, GDAL 3.8.2, PROJ 9.3.1; sf_use_s2() is TRUElibrary(sp) #Spatial Points function
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## combineWe obtained daily human-wildlife coexistence data between 2010-2021 in 35 selected Canadian national parks and historical sites from the Government of Canada Open Government database. Among the 9 recorded incident types, only those classified as “Human Wildlife Interaction” (HWI) were selected for. Incidents that involved unknown species or NA values were further omitted from the dataset, resulting in a total of 47,626 incidents for 152 species across the 12 years in 30 parks.
# importing data
animals_involved <- read.csv("data/hwi/pca-human-wildlife-coexistence-animals-involved-detailed-records-2010-2021.csv")
# filter out all the human wildlife interactions ----
HWI <- animals_involved %>%
filter(Incident.Type %in% c("Human Wildlife Interaction"))
# Cleaning the first nations heritage site in HWI data ----
HWI$Protected.Heritage.Area[HWI$Protected.Heritage.Area == "Saoy\xfa-?ehdacho National Historic Site of Canada"]<- "Grizzly Bear Mountain and Scented Grass Hills"
# Convert dates in HWI from characters to date ----
HWI$Incident.Date <- ymd(HWI$Incident.Date)
# Add a column "Incident Year" to HWI ----
HWI$Incident.Year <- as.numeric(format(HWI$Incident.Date, "%Y"))
# Add a colume "Incident Month" to HWI ----
HWI$Incident.Month <- as.numeric(format(HWI$Incident.Date, "%m"))
# Combine year and month into a single column
HWI$year_month <- as.yearmon(paste(HWI$Incident.Year, HWI$Incident.Month), "%Y %m")
# Renaming columns in HWI
HWI_parks <- HWI %>%
rename("park" = "Protected.Heritage.Area") %>%
rename("species" = "Species.Common.Name") %>%
rename("year" = "Incident.Year") %>%
rename("month" = "Incident.Month") %>%
rename("HWI" = "Incident.Type")
# Shortening park names
HWI_parks$park[HWI_parks$park == "Banff National Park of Canada"]<- "Banff"
HWI_parks$park[HWI_parks$park == "Pacific Rim National Park Reserve of Canada"]<- "Pacific_Rim"
HWI_parks$park[HWI_parks$park == "Waterton Lakes National Park of Canada"]<- "Waterton_Lakes"
HWI_parks$park[HWI_parks$park == "Kejimkujik National Park and National Historic Site of Canada"]<- "Kejimkujik"
HWI_parks$park[HWI_parks$park == "Jasper National Park of Canada"]<- "Jasper"
HWI_parks$park[HWI_parks$park == "Forillon National Park of Canada"]<- "Forillon"
HWI_parks$park[HWI_parks$park == "Prince Albert National Park of Canada"]<- "Prince_Albert"
HWI_parks$park[HWI_parks$park == "Kootenay National Park of Canada"]<- "Kootenay"
HWI_parks$park[HWI_parks$park == "Glacier National Park of Canada"]<- "Glacier"
HWI_parks$park[HWI_parks$park == "Wapusk National Park of Canada"]<- "Wapusk"
HWI_parks$park[HWI_parks$park == "Grasslands National Park of Canada"]<- "Grasslands"
HWI_parks$park[HWI_parks$park == "Bruce Peninsula National Park of Canada"]<- "Bruce_Peninsula"
HWI_parks$park[HWI_parks$park == "Yoho National Park of Canada"]<- "Yoho"
HWI_parks$park[HWI_parks$park == "Terra Nova National Park of Canada"]<- "Terra_Nova"
HWI_parks$park[HWI_parks$park == "Mount Revelstoke National Park of Canada"]<- "Mount_Revelstoke"
HWI_parks$park[HWI_parks$park == "Elk Island National Park of Canada"]<- "Elk_Island"
HWI_parks$park[HWI_parks$park == "Georgian Bay Islands National Park of Canada"]<- "Georgian_Bay_Islands"
HWI_parks$park[HWI_parks$park == "Prince of Wales Fort National Historic Site of Canada"]<- "Prince_of_Wales_Fort"
HWI_parks$park[HWI_parks$park == "Point Pelee National Park of Canada"]<- "Point_Pelee"
HWI_parks$park[HWI_parks$park == "Thousand Islands National Park of Canada"]<- "Thousand_Islands"
HWI_parks$park[HWI_parks$park == "Wood Buffalo National Park of Canada"]<- "Wood_Buffalo"
HWI_parks$park[HWI_parks$park == "Prince Edward Island National Park of Canada"]<- "Prince_Edward_Island"
HWI_parks$park[HWI_parks$park == "Ivvavik National Park of Canada"]<- "Ivvavik"
HWI_parks$park[HWI_parks$park == "Kouchibouguac National Park of Canada"]<- "Kouchibouguac"
HWI_parks$park[HWI_parks$park == "Grizzly Bear Mountain and Scented Grass Hills"]<- "Grizzly_Bear_Mountain"
HWI_parks$park[HWI_parks$park == "Fundy National Park of Canada"]<- "Fundy"
HWI_parks$park[HWI_parks$park == "Nahanni National Park Reserve of Canada"]<- "Nahanni"
HWI_parks$park[HWI_parks$park == "Aulavik National Park of Canada"]<- "Aulavik"
HWI_parks$park[HWI_parks$park == "Sable Island National Park Reserve"]<- "Sable_Island"
HWI_parks$park[HWI_parks$park == "Fathom Five National Marine Park of Canada"]<- "Fathom_Five"
HWI_parks$park[HWI_parks$park == "Fort Walsh National Historic Site of Canada"]<- "Fort_Walsh"
# Cleaning the species by omitting unknowns
HWI_parks <- HWI_parks[HWI_parks$species != "None",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown bear",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown bird",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown bat",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown ungulate",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown gull",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown canid",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown snake",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown fish",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown Duck",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown grouse",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown rodent",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown Myotis bat",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown raptor",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown owl",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown sea lion",]
HWI_parks <- HWI_parks[HWI_parks$species != "Unknown deer",]
# save HWI_parks ----
write.csv(HWI_parks, "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/old/hwi_parks.csv", row.names=FALSE)
HWI_parks <- read.csv("data/old/hwi_parks.csv")We explored the data by plotting a simple map using coordinates from Google Maps to visualise the locations of the parks, and grouped the incidents according to province, year, month, seasons, species for more data exploration.
#Count number of incidents by park
incident_count <- HWI_parks %>%
count(HWI_parks$park)
# import Canada shape and extract boundaries only
canadashape <- st_as_sf(PROV) %>%
st_geometry()
# import coordinates of all national parks, coordinates obtained from Google Maps
park_coordinates <- read.csv("data/park_coordinates.csv")
# convert coordinates into spatial data
park_location <- SpatialPoints(park_coordinates[, c("longitude", "latitude")])
# plot parks
plot(canadashape)
sp::plot(park_location, add = TRUE, col = 'coral', pch = 19, cex = 0.5) 
#Other visualisations ----
#Create another data frame by grouping according to months and years
HWI_grouped_date <- aggregate(HWI ~ year_month + park, data = HWI_parks, FUN = "length")
HWI_grouped_date$year_month <- as.yearmon(HWI_grouped_date$year_month)
HWI_grouped_date$year <- lubridate::year(HWI_grouped_date$year_month)
HWI_grouped_date$month <- lubridate::month(HWI_grouped_date$year_month)
# plot HWI across years and months ----
ggplot() +
geom_point(data = HWI_grouped_date, aes(x = year_month, y = HWI, col = park)) +
xlab("Time") +
ylab("Human-wildlife interactions") +
# using heat palette for parks
scale_color_manual(values = heatPalette(n=31)) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))## Warning: The `trans` argument of `continuous_scale()` is deprecated as of ggplot2 3.5.0.
## ℹ Please use the `transform` argument instead.
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## generated.
# group parks according to province ----
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Terra_Nova")] <- "NL"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Prince_Edward_Island")] <- "PE"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Kejimkujik", "Sable_Island")] <- "NS"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Kouchibouguac", "Fundy")] <- "NB"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Forillon")] <- "QC"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Bruce_Peninsula", "Fathom_Five", "Georgian_Bay_Islands", "Point_Pelee", "Thousand_Islands")] <- "ON"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Prince_of_Wales_Fort", "Wapusk")] <- "MB"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Prince_Albert")] <- "SK"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Banff", "Elk_Island", "Grasslands","Jasper", "Waterton_Lakes", "Wood_Buffalo")] <- "AB"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Glacier", "Kootenay", "Mount_Revelstoke", "Pacific_Rim", "Yoho")] <- "BC"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Ivvavik")] <- "YT"
HWI_grouped_date$park[HWI_grouped_date$park %in% c("Aulavik", "Grizzly_Bear_Mountain", "Nahanni")] <- "NT"
# plot parks according to province by month ----
HWI_province <- HWI_grouped_date %>%
rename("province" = "park")
ggplot() +
geom_point(data = HWI_province, aes(x = year_month, y = HWI, col = province), alpha = 0.25) +
xlab("Time") +
ylab("Human-wildlife interactions") +
# using rainbow palette for parks
scale_color_manual(values = rainbowPalette(n=12)) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
# plot species sightings ----
HWI_grouped_species <- aggregate(HWI ~ year_month + park + species + month + year, data = HWI_parks, FUN = "length")
ggplot() +
geom_point(data = HWI_grouped_species, aes(x = species, y = HWI, col = species), alpha = 0.8) +
xlab("Time") +
ylab("Human-wildlife interactions") +
# using rainbow palette for parks
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
#too much data
#still too much data
ggplot(data = HWI_grouped_species, aes(x = species, y = HWI)) +
geom_bar(stat = "identity", position = position_dodge(), width=0.5) +
scale_x_discrete(guide = guide_axis(n.dodge=1.5)) +
ylab("No. of Sightings") +
xlab("Species") +
theme(axis.text.x = element_text(angle = 90), axis.title.x = element_text(size=2, family = "sans", face = "bold"),)
# count no. of sightings per species
sightings <- HWI_grouped_species %>%
count(HWI_grouped_species$species)
# filter the sightings >10 by creating a subset (top 14 species)
filtered_sightings <- subset(HWI_grouped_species, HWI_grouped_species$HWI>10)
# plot species with >10 sightings (top 14 species) ----
ggplot(data = filtered_sightings, aes(x = species, y = HWI)) +
geom_bar(stat = "identity", position = position_dodge(), width=0.5) +
scale_x_discrete(guide = guide_axis(n.dodge=1.5)) +
ylab("No. of Sightings") +
xlab("Species") +
theme(axis.text.x = element_text(angle = 90), axis.title.x = element_text(size=2, family = "sans", face = "bold"),)
# plot species with >10 sightings (top 8 species) with time ----
ggplot() +
geom_point(data = filtered_sightings, aes(x = year_month, y = HWI, col = species), alpha = 0.8) +
xlab("Time") +
ylab("Frequency") +
# using rainbow palette for parks
scale_color_manual(values = rainbowPalette(n=14)) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
# plot HWI according to seasons ----
# creating a new dataset with seasons
HWI_with_season <- HWI_parks %>%
mutate(season = case_when(month %in% 3:5 ~ 'Spring',
month %in% 6:8 ~ 'Summer',
month %in% 9:11 ~ 'Autumn',
TRUE ~ 'Winter'))
#creating a new dataframe with seasons
HWI_grouped_season <- aggregate(HWI ~ year_month + park + species + season, data = HWI_with_season, FUN = "length")
HWI_grouped_season %>%
count(HWI_grouped_season$season)## HWI_grouped_season$season n
## 1 Autumn 1007
## 2 Spring 870
## 3 Summer 1914
## 4 Winter 437sum(HWI_grouped_season$HWI)## [1] 47626#plotting the number of HWI according to season
ggplot(data = HWI_grouped_season, aes(x = season, y = HWI)) +
geom_bar(stat = "identity", position = position_dodge(), width=0.5) +
scale_x_discrete(guide = guide_axis(n.dodge=1.5)) +
ylab("HWI Frequency") +
xlab("Season") +
theme(axis.title.x = element_text(size=8, family = "sans", face = "bold"),)
# filtering the species with >10 sightings ----
filtered_season_sightings <- subset(HWI_grouped_season, HWI_grouped_season$HWI>10)
# plotting the number of sightings of species >10 sightings according to season ----
ggplot() +
geom_point(data = filtered_season_sightings, aes(x = season, y = HWI, col = species), alpha = 0.8) +
xlab("Season") +
ylab("No. of Sightings") +
# using rainbow palette for parks
scale_color_manual(values = rainbowPalette(n=14)) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
A Poisson generalized additive model (GAM) was fitted to the data of Jasper National Park to visualize the normal trend of HWIs across the years, with park and species included as random effects to account for the variability.
# models for visualising the normal trend ----
HWI_grouped_species <- HWI_grouped_species %>%
mutate(park = factor(park))
HWI_grouped_species$species <- as.factor(HWI_grouped_species$species)
model1 <- gam(HWI ~
s(park, bs = "fs") +
s(species, bs = "fs") +
#Add a random effect for species
ti(year, park, k = 12, bs = "fs") +
#Adjust for a random effect of park, done
ti(month, park, k = 8, bs = "fs"),
family = "poisson",
data = HWI_grouped_species, method = "REML")
summary(model1)
plot(model1, pages = 1)# residuals of model 1
head(residuals(model1))## [1] 2.8019929 0.6012772 -3.3510490 1.6916838 1.2541619 1.2316972# add the residuals as a new column into the HWI_grouped_species dataframe ----
HWI_grouped_species$residuals <- residuals(model1)
# looking at the distribution of the residuals
hist(HWI_grouped_species$residuals)
#look at the trend in Jasper ----
Jasper_trend <- HWI_grouped_species %>%
filter(park %in% c("Jasper"))
#plot the trend of residuals by year in Jasper ----
ggplot() +
geom_hline(aes(yintercept = 0), col = "grey70", linetype = "dashed") +
geom_point(data = Jasper_trend, aes(x = year_month, y = residuals, col = species)) +
xlab("Date") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "none",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
# Look at the trend of residuals by month in Jasper ----
Jasper_jan_trend <- Jasper_trend %>%
filter(month %in% c("1"))
Jasper_feb_trend <- Jasper_trend %>%
filter(month %in% c("2"))
Jasper_mar_trend <- Jasper_trend %>%
filter(month %in% c("3"))
Jasper_apr_trend <- Jasper_trend %>%
filter(month %in% c("4"))
Jasper_may_trend <- Jasper_trend %>%
filter(month %in% c("5"))
Jasper_jun_trend <- Jasper_trend %>%
filter(month %in% c("6"))
Jasper_jul_trend <- Jasper_trend %>%
filter(month %in% c("7"))
Jasper_aug_trend <- Jasper_trend %>%
filter(month %in% c("8"))
Jasper_sep_trend <- Jasper_trend %>%
filter(month %in% c("9"))
Jasper_oct_trend <- Jasper_trend %>%
filter(month %in% c("10"))
Jasper_nov_trend <- Jasper_trend %>%
filter(month %in% c("11"))
Jasper_dec_trend <- Jasper_trend %>%
filter(month %in% c("12"))
# plot the monthly residual trend data in Jasper by year ----
ggplot() +
geom_point(data = Jasper_jan_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_feb_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_mar_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_apr_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_may_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_jun_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_jul_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_aug_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_sep_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_oct_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_nov_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggplot() +
geom_point(data = Jasper_dec_trend, aes(x = year, y = residuals)) +
xlab("Year") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
To prepare for modelling, we obtained polygons for the National Parks
and National Park Reserves of Canada Legislative Boundaries from the
Government of Canada Open Government database. Among the 30 sites
recorded in the HWI data, boundaries for 5 of them were unavailable.
These sites were excluded from the analysis. Our final study area
therefore consists of 25 parks across the country.
# importing polygons with sf ----
ABpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_AB_2023-09-08/CLAB_AB_2023-09-08.shp")## Reading layer `CLAB_AB_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_AB_2023-09-08\CLAB_AB_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 5 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -119.5439 ymin: 48.9975 xmax: -111.017 ymax: 60.69088
## Geodetic CRS: NAD83(CSRS)plot(ABpolygon)
saveRDS(ABpolygon,file ="data/old/ABpolygon.rds")
BCpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_BC_2023-09-08/CLAB_BC_2023-09-08.shp")## Reading layer `CLAB_BC_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_BC_2023-09-08\CLAB_BC_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 7 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -132.1088 ymin: 48.53914 xmax: -115.7991 ymax: 52.8101
## Geodetic CRS: NAD83(CSRS)plot(BCpolygon)
saveRDS(BCpolygon,file ="data/old/BCpolygon.rds")
MBpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_MB_2023-09-08/CLAB_MB_2023-09-08.shp")## Reading layer `CLAB_MB_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_MB_2023-09-08\CLAB_MB_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 2 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -101.0929 ymin: 50.50642 xmax: -92.32702 ymax: 58.80892
## Geodetic CRS: NAD83(CSRS)plot(MBpolygon)
saveRDS(MBpolygon,file ="data/old/MBpolygon.rds")
NBpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_NB_2023-09-08/CLAB_NB_2023-09-08.shp")## Reading layer `CLAB_NB_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_NB_2023-09-08\CLAB_NB_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 2 features and 8 fields
## Geometry type: POLYGON
## Dimension: XY
## Bounding box: xmin: -65.15165 ymin: 45.52535 xmax: -64.78989 ymax: 46.96371
## Geodetic CRS: NAD83(CSRS)plot(NBpolygon)
saveRDS(NBpolygon,file ="data/old/NBpolygon.rds")
NLpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_NL_2023-09-08/CLAB_NL_2023-09-08.shp")## Reading layer `CLAB_NL_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_NL_2023-09-08\CLAB_NL_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 3 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -64.93944 ymin: 48.38653 xmax: -53.68841 ymax: 60.37774
## Geodetic CRS: NAD83(CSRS)plot(NLpolygon)
saveRDS(NLpolygon,file ="data/old/NLpolygon.rds")
NSpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_NS_2023-09-08/CLAB_NS_2023-09-08.shp")## Reading layer `CLAB_NS_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_NS_2023-09-08\CLAB_NS_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 2 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -65.451 ymin: 43.81315 xmax: -60.31676 ymax: 46.86432
## Geodetic CRS: NAD83(CSRS)plot(NSpolygon)
saveRDS(NSpolygon,file ="data/old/NSpolygon.rds")
NTpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_NT_2023-09-08/CLAB_NT_2023-09-08.shp")## Reading layer `CLAB_NT_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_NT_2023-09-08\CLAB_NT_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 6 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -129.7853 ymin: 58.07851 xmax: -106.6059 ymax: 74.48389
## Geodetic CRS: NAD83(CSRS)plot(NTpolygon)
saveRDS(NTpolygon,file ="data/old/NTpolygon.rds")
NUpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_NU_2023-09-08/CLAB_NU_2023-09-08.shp")## Reading layer `CLAB_NU_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_NU_2023-09-08\CLAB_NU_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 5 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -104.4771 ymin: 65.01667 xmax: -62.51257 ymax: 83.15754
## Geodetic CRS: NAD83(CSRS)plot(NUpolygon)
saveRDS(NUpolygon,file ="data/old/NUpolygon.rds")
ONpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_ON_2023-09-08/CLAB_ON_2023-09-08.shp")## Reading layer `CLAB_ON_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_ON_2023-09-08\CLAB_ON_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 5 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -82.6884 ymin: 41.68132 xmax: -75.71257 ymax: 45.32816
## Geodetic CRS: NAD83(CSRS)plot(ONpolygon)
saveRDS(ONpolygon,file ="data/old/ONpolygon.rds")
PEpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_PE_2023-09-08/CLAB_PE_2023-09-08.shp")## Reading layer `CLAB_PE_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_PE_2023-09-08\CLAB_PE_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 1 feature and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -63.47902 ymin: 46.40307 xmax: -62.96987 ymax: 46.51147
## Geodetic CRS: NAD83(CSRS)plot(PEpolygon)
saveRDS(PEpolygon,file ="data/old/PEpolygon.rds")
QCpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_QC_2023-09-08/CLAB_QC_2023-09-08.shp")## Reading layer `CLAB_QC_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_QC_2023-09-08\CLAB_QC_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 4 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -73.17896 ymin: 46.6465 xmax: -62.1155 ymax: 50.30949
## Geodetic CRS: NAD83(CSRS)plot(QCpolygon)
saveRDS(QCpolygon,file ="data/old/QCpolygon.rds")
SKpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_SK_2023-09-08/CLAB_SK_2023-09-08.shp")## Reading layer `CLAB_SK_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_SK_2023-09-08\CLAB_SK_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 2 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -107.7324 ymin: 49.00007 xmax: -106.0036 ymax: 54.34495
## Geodetic CRS: NAD83(CSRS)plot(SKpolygon)
saveRDS(SKpolygon,file ="data/old/SKpolygon.rds")
YTpolygon <- st_read("data/shapefiles/ca_provinces/CLAB_YT_2023-09-08/CLAB_YT_2023-09-08.shp")## Reading layer `CLAB_YT_2023-09-08' from data source
## `C:\Users\grace\Documents\GitHub\HWI_NDVI_parks\data\shapefiles\ca_provinces\CLAB_YT_2023-09-08\CLAB_YT_2023-09-08.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 4 features and 8 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -141.002 ymin: 59.99964 xmax: -137.0174 ymax: 69.64783
## Geodetic CRS: NAD83(CSRS)plot(YTpolygon)
saveRDS(YTpolygon,file ="data/old/YTpolygon.rds")
# fitering for my 30 parks out of all the parks in each polygon ----
#AB
waterton_lakes <- ABpolygon[ABpolygon$CLAB_ID == "WATE", ]
plot(waterton_lakes)
saveRDS(waterton_lakes,file ="data/old/waterton_lakes.rds")
elk_island <- ABpolygon[ABpolygon$CLAB_ID == "ELKI", ]
plot(elk_island)
saveRDS(elk_island,file ="data/old/elk_island.rds")
jasper <- ABpolygon[ABpolygon$CLAB_ID == "JASP", ]
plot(jasper)
saveRDS(jasper,file ="data/old/jasper.rds")
wood_buffalo <- ABpolygon[ABpolygon$CLAB_ID == "WOOD", ]
plot(wood_buffalo)
saveRDS(wood_buffalo,file ="data/old/wood_buffalo.rds")
banff <- ABpolygon[ABpolygon$CLAB_ID == "BANF", ]
plot(banff)
saveRDS(banff,file ="data/old/banff.rds")
# no polygon for grasslands
# BC
yoho <- BCpolygon[BCpolygon$CLAB_ID == "YOHO", ]
plot(yoho)
saveRDS(yoho,file ="data/old/yoho.rds")
kootenay <- BCpolygon[BCpolygon$CLAB_ID == "KOOT", ]
plot(kootenay)
saveRDS(kootenay,file ="data/old/kootenay.rds")
mount_revelstoke <- BCpolygon[BCpolygon$CLAB_ID == "REVE", ]
plot(mount_revelstoke)
saveRDS(mount_revelstoke,file ="data/old/mount_revelstoke.rds")
pacific_rim <- BCpolygon[BCpolygon$CLAB_ID == "PRIM", ]
plot(pacific_rim)
saveRDS(pacific_rim,file ="data/old/pacific_rim.rds")
glacier <- BCpolygon[BCpolygon$CLAB_ID == "GLAC", ]
plot(glacier)
saveRDS(glacier,file ="data/old/glacier.rds")
# MB
wapusk <- MBpolygon[MBpolygon$CLAB_ID == "WAPU", ]
plot(wapusk)
saveRDS(wapusk,file ="data/old/wapusk.rds")
# no polygon for prince of wales fort
# NB
fundy <- NBpolygon[NBpolygon$CLAB_ID == "FUND", ]
plot(fundy)
saveRDS(fundy,file ="data/old/fundy.rds")
kouchibouguac <- NBpolygon[NBpolygon$CLAB_ID == "KOUC", ]
plot(kouchibouguac)
saveRDS(kouchibouguac,file ="data/old/kouchibouguac.rds")
# NL
terra_nova <- NLpolygon[NLpolygon$CLAB_ID == "NOVA", ]
plot(terra_nova)
saveRDS(terra_nova,file ="data/old/terra_nova.rds")
# NS
kejimkujik <- NSpolygon[NSpolygon$CLAB_ID == "KEJI", ]
plot(kejimkujik)
saveRDS(kejimkujik,file ="data/old/kejimkijik.rds")
# no polygon on sable island
# NT
aulavik <- NTpolygon[NTpolygon$CLAB_ID == "AULA", ]
plot(aulavik)
saveRDS(aulavik,file ="data/old/aulavik.rds")
nahanni <- NTpolygon[NTpolygon$CLAB_ID == "NAHA", ]
plot(nahanni)
saveRDS(nahanni,file ="data/old/nahanni.rds")
# no polygon for grizzly bear
# no NU parks in my data
#ON
fathom_five <- ONpolygon[ONpolygon$CLAB_ID == "FIVE", ]
plot(fathom_five)
saveRDS(fathom_five,file ="data/old/fathom_five.rds")
point_pelee <- ONpolygon[ONpolygon$CLAB_ID == "PELE", ]
plot(point_pelee)
saveRDS(point_pelee,file ="data/old/point_pelee.rds")
georgian_bay_islands <- ONpolygon[ONpolygon$CLAB_ID == "GBIS", ]
plot(georgian_bay_islands)
saveRDS(georgian_bay_islands,file ="data/old/georgian_bay_islands.rds")
thousand_islands <- ONpolygon[ONpolygon$CLAB_ID == "THIS", ]
plot(thousand_islands)
saveRDS(thousand_islands,file ="data/old/thousand_islands.rds")
# no polygon for bruce peninsula
# PE
prince_edward_island <- PEpolygon[PEpolygon$CLAB_ID == "PEIS", ]
plot(prince_edward_island)
saveRDS(prince_edward_island,file ="data/old/prince_edward_island.rds")
# QC
forillon <- QCpolygon[QCpolygon$CLAB_ID == "FORI", ]
plot(forillon)
saveRDS(forillon,file ="data/old/forillon.rds")
# SK
prince_albert <- SKpolygon[SKpolygon$CLAB_ID == "PALB", ]
plot(prince_albert)
saveRDS(prince_albert,file ="data/old/prince_albert.rds")
# YT
ivvavik <- YTpolygon[YTpolygon$CLAB_ID == "IVVA", ]
plot(ivvavik)
saveRDS(ivvavik,file ="data/old/ivvavik.rds")
# 5 parks do not have polygonsUsing the 25 parks, we plotted a map to visualise all the study sites across the country.
# new map ----
# import coordinates of all national parks, coordinates obtained from Google Maps
park_coordinates <- read.csv("data/park_coordinates.csv")
# remove the dropped parks x5
parks_to_drop <- c("Grasslands National Park of Canada", "Bruce Peninsula National Park of Canada", "Prince of Wales Fort National Historic Site of Canada", "Saoy\\xfa-?ehdacho National Historic Site of Canada", "Sable Island National Park Reserve", "Fort Walsh National Historic Site of Canada")
new_park_coordinates <- subset(park_coordinates, !(park %in% parks_to_drop))
# match coordinates name to park ID
new_park_coordinates$park[new_park_coordinates$park == "Banff National Park of Canada"]<- "BANF"
new_park_coordinates$park[new_park_coordinates$park == "Pacific Rim National Park Reserve of Canada"]<- "PRIM"
new_park_coordinates$park[new_park_coordinates$park == "Waterton Lakes National Park of Canada"]<- "WATE"
new_park_coordinates$park[new_park_coordinates$park == "Kejimkujik National Park and National Historic Site of Canada"]<- "KEJI"
new_park_coordinates$park[new_park_coordinates$park == "Jasper National Park of Canada"]<- "JASP"
new_park_coordinates$park[new_park_coordinates$park == "Forillon National Park of Canada"]<- "FORI"
new_park_coordinates$park[new_park_coordinates$park == "Prince Albert National Park of Canada"]<- "PALB"
new_park_coordinates$park[new_park_coordinates$park == "Kootenay National Park of Canada"]<- "KOOT"
new_park_coordinates$park[new_park_coordinates$park == "Glacier National Park of Canada"]<- "GLAC"
new_park_coordinates$park[new_park_coordinates$park == "Wapusk National Park of Canada"]<- "WAPU"
new_park_coordinates$park[new_park_coordinates$park == "Yoho National Park of Canada"]<- "YOHO"
new_park_coordinates$park[new_park_coordinates$park == "Terra Nova National Park of Canada"]<- "NOVA"
new_park_coordinates$park[new_park_coordinates$park == "Mount Revelstoke National Park of Canada"]<- "REVE"
new_park_coordinates$park[new_park_coordinates$park == "Elk Island National Park of Canada"]<- "ELKI"
new_park_coordinates$park[new_park_coordinates$park == "Georgian Bay Islands National Park of Canada"]<- "GBIS"
new_park_coordinates$park[new_park_coordinates$park == "Point Pelee National Park of Canada"]<- "PELE"
new_park_coordinates$park[new_park_coordinates$park == "Thousand Islands National Park of Canada"]<- "THIS"
new_park_coordinates$park[new_park_coordinates$park == "Wood Buffalo National Park of Canada"]<- "WOOD"
new_park_coordinates$park[new_park_coordinates$park == "Prince Edward Island National Park of Canada"]<- "PEIS"
new_park_coordinates$park[new_park_coordinates$park == "Ivvavik National Park of Canada"]<- "IVVA"
new_park_coordinates$park[new_park_coordinates$park == "Kouchibouguac National Park of Canada"]<- "KOUC"
new_park_coordinates$park[new_park_coordinates$park == "Fundy National Park of Canada"]<- "FUND"
new_park_coordinates$park[new_park_coordinates$park == "Nahanni National Park Reserve of Canada"]<- "NAHA"
new_park_coordinates$park[new_park_coordinates$park == "Aulavik National Park of Canada"]<- "AULA"
new_park_coordinates$park[new_park_coordinates$park == "Fathom Five National Marine Park of Canada"]<- "FIVE"
# convert coordinates into spatial data
new_park_location <- SpatialPoints(new_park_coordinates[, c("longitude", "latitude")])
parks_sf <- st_as_sf(new_park_coordinates, coords = c("longitude", "latitude"), crs = 4326)
#define the crs
esri_102001 <- st_crs("+proj=aea +lat_1=20 +lat_2=60 +lat_0=40 +lon_0=-96 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs")
# reproject parks coordinate
parks_esri <- st_transform(parks_sf, crs = esri_102001)
#convert back to dataframe
parks_esri_df <- st_drop_geometry
#convert to coordinates
coordinates <- st_coordinates(parks_esri)
# combine reprojected esri coordinates into original coordinates df
park_coordinates_esri <- cbind(coordinates, new_park_coordinates)
# renaming the columns
names(park_coordinates_esri)[1] <- "esri_long"
names(park_coordinates_esri)[2] <- "esri_lat"# Canada map ----
#level 0 = country; level 1 = province/state; level 2 = counties
provinces <- gadm(country="Canada", level=1, path = tempdir())
#save as an RDS
saveRDS(provinces,file ="data/shapefiles/CAprovinces_map.rds")
provinces <- readRDS("data/shapefiles/CAprovinces_map.rds")#plot both shape files, layered
plot(provinces)
# import ndvi file
ndvi_bg <- "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2021ndvi/2021_jun/VIIRS-Land_v001-preliminary_NPP13C1_S-NPP_20210630_c20220419155820.nc"
ndvi_bg <- terra::rast(ndvi_bg) #bg is 2021 jun 30
plot(ndvi_bg$NDVI)
# reproject NDVI to provinces crs
reprojected_bg <- terra::project(ndvi_bg,
provinces,
method = "near")
#crop reprojected ndvi bg to Can shape
cropped_provinces_ndvi <- crop(reprojected_bg, provinces, mask = TRUE)
provinces_bg <- cropped_provinces_ndvi$NDVI
saveRDS(provinces_bg,file ="figures/old_figures/Canmap.rds")
provinces_bg <- readRDS("figures/old_figures/Canmap.rds")#find the extent of the raster
ext(provinces_bg)## SpatExtent : -141.000005509252, -52.6000041603337, 41.6999988824795, 83.0999985311861 (xmin, xmax, ymin, ymax)#set the bounding box
bbox <- ext(c(-141.006866, -52.6000041603337, 41.6999988824795, 83.0999985311861))
#crop the ndvi
bg_crop <- crop(provinces_bg, bbox)
#write raster
writeRaster(bg_crop, "figures/old_figures/bg_crop.tif", overwrite = TRUE)#REPROJECT BG_CROP
bg_reproject <- terra::project(bg_crop,
"ESRI:102001")plot(bg_crop)
saveRDS(bg_crop,file ="figures/old_figures/bg_crop.rds")
#crop the map
Can_crop <- crop(provinces, bbox)## intersection 0 done
## intersection 1 done
## intersection 2 done
## intersection 3 done
## intersection 4 done
## intersection 5 done
## intersection 6 done
## intersection 7 done
## intersection 8 done
## intersection 9 done
## intersection 10 done
## intersection 11 done
## intersection 12 donesaveRDS(Can_crop,file ="figures/old_figures/Can_crop.rds")
Can_crop <- readRDS("figures/old_figures/Can_crop.rds")
plot(Can_crop)
# Define manual color scale due to adding national parks ----
manual_colors <- c("WATE"= "#560133", "ELKI" = "#790149", "JASP" = "#9F0162", "WOOD" = "#C7007C",
"BANF" = "#EF0096", "YOHO" = "#FF5AAF", "KOOT" = "#FF9DCB", "REVE" = "#FFCFF2",
"PRIM" = "#450270", "GLAC" = "#65019F", "WAPU" = "#8400CD", "FUND" = "#A700FC",
"KOUC" = "#DA00FD", "NOVA" = "#FF3CFE", "KEJI" = "#FF92FD", "AULA" = "#FFCCFE",
"NAHA" = "#5A000F", "FIVE" = "#7E0018", "PELE" = "#A40122", "GBIS" = "#CD022D",
"THIS" = "#F60239", "PEIS" = "#FF6E3A", "FORI" = "#FFAC3B", "PALB" = "#FFDC3D", "IVVA" = "#FF4C30")
# Plotting the map
provinces_sf <- st_as_sf(Can_crop)#NDVI colour palette
NDVI_cols <- colorRampPalette(rev(c("#0f2902", "#1d3900","#193401","#274009","#2e4511",
"#3d4f21", "#485921","#536321","#69761f","#868924",
"#8d8e37","#aaa263","#b5a975","#c2b58c","#c7b995",
"#cdbf9f","#e3d6c6","#e7dbce")))
#plot map withESRI:102001 projection
reprojected_new_map <-
ggplot() +
geom_spatraster(data = bg_reproject, alpha = 0.8, maxcell = 5e+08) + #ndvi bg
scale_fill_gradientn(name = "Normalized Difference Vegetation Index",
colours = NDVI_cols(255),
na.value = NA,
breaks = c(11, 63.75, 127.50, 191.25, 254.00),
labels = c(-1.0, -0.5, 0.0, 0.5, 1.0)) +
geom_sf(data = provinces_sf, fill = "transparent", color = "black", size = 1) + #map
geom_point(data = park_coordinates_esri, aes(x = esri_long, y = esri_lat, col = park, shape = park),
size = 3, alpha = 0.8) +
guides(col = guide_legend(override.aes = list(alpha=0.8,
shape = rep(17,25))),
shape = "none", alpha = "none") +
scale_colour_manual(name="Park",
values = manual_colors) +
scale_shape_manual(values = rep(17,25)) +
theme(
panel.background = element_rect(fill="transparent"), #transparent panel bg
plot.background = element_rect(fill="transparent", color=NA), #transparent plot bg
panel.grid.major = element_blank(), #remove major gridlines
panel.grid.minor = element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank(),
axis.title.x = element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank(),
axis.title.y = element_blank(),
legend.title = element_text(size = 11, face = "bold"),
legend.text = element_text(size = 11),
legend.position = "none",
legend.justification = "center",
legend.direction = "vertical",
#legend.box.background = element_rect(color = "black"),
plot.margin = unit(c(-1,0,-1,0), "cm"),
plot.title = element_text(vjust = -8.5, hjust = 0.03,
size = 30, family = "sans", face = "bold")) +
coord_sf() # ensures points don't get jittered around when figure dimensions change
ggsave(reprojected_new_map, filename = "figures/new_map_reprojected.png", width = 6.86, height = 6, units = "in", dpi = 600, background ="transparent")We obtained daily ADVRR NDVI data of 5km resolution between 2010-2021 from the NOAA Climate Data Record.
# loop for extracting all links for 2010 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2010/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2010ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
#test the files to see if they can plot ndvi
file1 <- "2010ndvi/2010_jan/AVHRR-Land_v005_AVH13C1_NOAA-19_20100101_c20170406091314.nc"
file2 <- "2010ndvi/2010_dec/AVHRR-Land_v005_AVH13C1_NOAA-19_20101231_c20170406211535.nc"
NDVI <- terra::rast(file1)
plot(NDVI$NDVI)
# download 2011-2021 data ----
# loop for extracting all links for 2011 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2011/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2011ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2012 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2012/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2012ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2013 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2013/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2013ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2014 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2014/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2014ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2015 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2015/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2015ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2016 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2016/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2016ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2017 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2017/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2017ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2018 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2018/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2018ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2019 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2019/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2019ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2020 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2020/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2020ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for extracting all links for 2021 ----
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2021/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2021ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}The NDVI data was cropped to the boundaries of each park, and their monthly means were taken.
# for loop for cropping all the ndvi data into the park polygons and take monthly mean
nc.year_dir <- "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/ndvi"
# setwd(nc.year_dir)
# import all of the boundaries for Canadian parks
CAshape <- st_read("data/shapefiles/ca_provinces/CLAB_CA_2023-09-08")
# Create a list of the names of the 25 parks to be studied
test_parks <- c("WATE", "ELKI", "JASP", "WOOD",
"BANF", "YOHO", "KOOT", "REVE",
"PRIM", "GLAC", "WAPU", "FUND",
"KOUC", "NOVA", "KEJI", "AULA",
"NAHA", "FIVE", "PELE", "GBIS",
"THIS", "PEIS", "FORI", "PALB", "IVVA")
# import JASP shapefile
jasper_shape <- readRDS("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/shapefiles/parks_polygons/jasper.rds")
# Define the CRS
CRS_canada <- crs(jasper_shape)
# List all year folders in the ndvi directory
year_folders <- list.dirs(path = nc.year_dir, full.names = TRUE, recursive = FALSE)
RESULTS <- list()
# Loop through each year folder
for (i in 1:length(year_folders)) { #length(year_folders)
year <- gsub(pattern = "ndvi",
replacement = "",
x = gsub(pattern = "data/ndvi/",
replacement = "",
x = year_folders[i]))
# List all month folders in the year folder
month_folders <- list.dirs(path = year_folders[i],
full.names = TRUE,
recursive = FALSE)
# Generate an empty list for storing daily results
res_month <- list()
# Loop through each month folder
for (j in 1:length(month_folders)) {
# Make a list of the files in the month directory
nc.files <- list.files(path = month_folders[j],
pattern = "*.nc",
full.names = TRUE)
# Generate an empty list for storing daily results
res_day <- list()
# Loop through all the ndvi files for the current month
for (k in 1:length(nc.files)) {
# make the spatrasters
spat <- rast(nc.files[k])
spat <- spat[[which(names(spat) == "NDVI")]]
# Reproject the raster to the CRS of jasper_shape
reprojected_spat <- terra::project(spat,
CRS_canada,
method = "near")
# Generate an empty list for storing results
res <- list()
#Loop over the vector of park names to extract the NDVI information
for(l in 1:length(test_parks)){
#Extract the desired park contour
PARK <- CAshape[CAshape$CLAB_ID %in% test_parks[l],]
# crop the NDVI raster to the park
cropped_spat <- crop(reprojected_spat, PARK, mask = TRUE)
# Get mean and variance in NDVI
NDVI <- mean(values(cropped_spat), na.rm = TRUE)
#NDVI_var <- var(cropped_spat)
NDVI_var <- var(values(cropped_spat), na.rm = TRUE)
# Store as a data frame in the list
res[[l]] <- data.frame(park = test_parks[l],
date = paste(year,j,k,sep = "_"),
ndvi = NDVI,
ndvi_var = NDVI_var)
} #close the loop over parks
#clean up the results over the days of the month
res_day[[k]] <- do.call(rbind,res)
} #close of day loop
#clean up the results over the months of the year
res_month[[j]] <- do.call(rbind,res_day)
} # close of the month loop
#clean up the results over the months of the year
RESULTS[[i]] <- do.call(rbind,res_month)
} # close of year loop
# convert the final list to a data frame (daily ndvi mean and var)
RESULTS <- do.call(rbind,RESULTS)
#save as CSV
write.csv(RESULTS, "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/parksndvi.csv", row.names=FALSE)
RESULTS_df <- read.csv("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/parksndvi.csv")
# close loop of all the years We scaled the NDVI values to positive using the formula (monthly mean NDVI + 1)/2 for modelling. We built a generalized additive model (GAM) with a beta distribution using the mgcv R package, with parks as a fixed effect, and month and park, year and park, and the interaction between month and year as smooth terms to understand the changes in NDVI based on these variables.
# results dataframe (2010-2021)----
#Create data frame by grouping park means according to months and years
#convert to calendar dates
RESULTS_df$date <- as.Date(RESULTS_df$date, format = "%Y_%m_%d")
#extract year
RESULTS_df$year <- lubridate::year(RESULTS_df$date)
#extract month
RESULTS_df$month <- lubridate::month(RESULTS_df$date)
#rename columns
names(RESULTS_df)[3] <- "ndvi_daily_mean"
names(RESULTS_df)[4] <- "ndvi_daily_variance"
# Create a new dataframe for analysis for monthly ndvi mean to be grouped by park and year
data_ndvi_mean <- aggregate(ndvi_daily_mean ~ month + year + park, data = RESULTS_df, FUN = mean, na.rm = TRUE)
#rename columns
names(data_ndvi_mean)[4] <- "ndvi_monthly_mean"
#save datafram as a csv
write.csv(data_ndvi_mean, "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/monthly_mean_ndvi.csv", row.names=FALSE)
mean_ndvi_df <- read.csv("data/models/model_results/monthly_mean_ndvi.csv")
# rescale ndvi in dataframe to 0-1 for beta gam
mean_ndvi_df <- mean_ndvi_df %>%
mutate((ndvi_monthly_mean+1)/2)
# rename columns
names(mean_ndvi_df)[5] <- "scaled_mean_ndvi"
# change month and year to numeric
as.numeric(mean_ndvi_df$month)## [1] 1 2 4 6 7 8 9 11 12 1 2 4 6 7 8 9 11 12 1 2 4 6 7 8
## [25] 9 11 12 1 2 4 6 7 8 9 11 12 1 2 4 6 7 8 9 11 12 1 2 4
## [49] 6 7 8 9 11 12 1 2 4 6 7 8 9 11 12 1 2 4 6 7 8 9 11 12
## [73] 1 2 4 6 7 8 9 11 12 1 2 4 6 7 8 9 11 12 1 2 4 6 7 8
## [97] 9 11 12 1 2 4 6 7 8 9 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [121] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [145] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [169] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [193] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [217] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [241] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [265] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [289] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [313] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [337] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [361] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [385] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [409] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [433] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [457] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [481] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [505] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [529] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [553] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [577] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [601] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [625] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [649] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [673] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [697] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [721] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [745] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [769] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [793] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [817] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [841] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [865] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [889] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [913] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [937] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [961] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [985] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1009] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1033] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1057] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1081] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1105] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 4 6 7 8 9 10 11 12 1 2
## [1129] 4 6 7 8 9 10 11 12 1 2 4 6 7 8 9 10 11 12 1 2 4 6 7 8
## [1153] 9 10 11 12 1 2 4 6 7 8 9 10 11 12 1 2 4 6 7 8 9 10 11 12
## [1177] 1 2 4 6 7 8 9 10 11 12 1 2 4 6 7 8 9 10 11 12 1 2 4 6
## [1201] 7 8 9 10 11 12 1 2 4 6 7 8 9 10 11 12 1 2 4 6 7 8 9 10
## [1225] 11 12 1 2 4 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1249] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1273] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1297] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1321] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1345] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1369] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1393] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1417] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1441] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1465] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1489] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1513] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1537] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1561] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1585] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1609] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1633] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1657] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1681] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1705] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1729] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1753] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1777] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1801] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1825] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1849] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1873] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1897] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1921] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1945] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1969] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [1993] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2017] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2041] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2065] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2089] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2113] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2137] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2161] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2185] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2209] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2233] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2257] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2281] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2305] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2329] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2353] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2377] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2401] 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
## [2425] 1 2 3 4 5 6 7 8 9 10 11 12 7 8 9 5 5 6 7 9 11 4 12 6
## [2449] 2 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2473] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2497] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2521] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2545] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2569] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2593] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2617] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2641] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2665] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2689] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2713] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2737] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2761] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2785] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2809] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2833] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2857] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2881] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2905] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2929] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2953] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [2977] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3001] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3025] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3049] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3073] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3097] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3121] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3145] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3169] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3193] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3217] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3241] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3265] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3289] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3313] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3337] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3361] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3385] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3409] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3433] 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
## [3457] 12as.numeric(mean_ndvi_df$year)## [1] 2010 2010 2010 2010 2010 2010 2010 2010 2010 2011 2011 2011 2011 2011
## [15] 2011 2011 2011 2011 2012 2012 2012 2012 2012 2012 2012 2012 2012 2013
## [29] 2013 2013 2013 2013 2013 2013 2013 2013 2014 2014 2014 2014 2014 2014
## [43] 2014 2014 2014 2015 2015 2015 2015 2015 2015 2015 2015 2015 2016 2016
## [57] 2016 2016 2016 2016 2016 2016 2016 2017 2017 2017 2017 2017 2017 2017
## [71] 2017 2017 2018 2018 2018 2018 2018 2018 2018 2018 2018 2019 2019 2019
## [85] 2019 2019 2019 2019 2019 2019 2020 2020 2020 2020 2020 2020 2020 2020
## [99] 2020 2021 2021 2021 2021 2021 2021 2021 2021 2021 2010 2010 2010 2010
## [113] 2010 2010 2010 2010 2010 2010 2010 2010 2011 2011 2011 2011 2011 2011
## [127] 2011 2011 2011 2011 2011 2011 2012 2012 2012 2012 2012 2012 2012 2012
## [141] 2012 2012 2012 2012 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013
## [155] 2013 2013 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014
## [169] 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2016 2016
## [183] 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016 2017 2017 2017 2017
## [197] 2017 2017 2017 2017 2017 2017 2017 2017 2018 2018 2018 2018 2018 2018
## [211] 2018 2018 2018 2018 2018 2018 2019 2019 2019 2019 2019 2019 2019 2019
## [225] 2019 2019 2019 2019 2020 2020 2020 2020 2020 2020 2020 2020 2020 2020
## [239] 2020 2020 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021
## [253] 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2011 2011
## [267] 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2012 2012 2012 2012
## [281] 2012 2012 2012 2012 2012 2012 2012 2012 2013 2013 2013 2013 2013 2013
## [295] 2013 2013 2013 2013 2013 2013 2014 2014 2014 2014 2014 2014 2014 2014
## [309] 2014 2014 2014 2014 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015
## [323] 2015 2015 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016
## [337] 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2018 2018
## [351] 2018 2018 2018 2018 2018 2018 2018 2018 2018 2018 2019 2019 2019 2019
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## [421] 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2013 2013
## [435] 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2014 2014 2014 2014
## [449] 2014 2014 2014 2014 2014 2014 2014 2014 2015 2015 2015 2015 2015 2015
## [463] 2015 2015 2015 2015 2015 2015 2016 2016 2016 2016 2016 2016 2016 2016
## [477] 2016 2016 2016 2016 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017
## [491] 2017 2017 2018 2018 2018 2018 2018 2018 2018 2018 2018 2018 2018 2018
## [505] 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2020 2020
## [519] 2020 2020 2020 2020 2020 2020 2020 2020 2020 2020 2021 2021 2021 2021
## [533] 2021 2021 2021 2021 2021 2021 2021 2021 2010 2010 2010 2010 2010 2010
## [547] 2010 2010 2010 2010 2010 2010 2011 2011 2011 2011 2011 2011 2011 2011
## [561] 2011 2011 2011 2011 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012
## [575] 2012 2012 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013
## [589] 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2015 2015
## [603] 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2016 2016 2016 2016
## [617] 2016 2016 2016 2016 2016 2016 2016 2016 2017 2017 2017 2017 2017 2017
## [631] 2017 2017 2017 2017 2017 2017 2018 2018 2018 2018 2018 2018 2018 2018
## [645] 2018 2018 2018 2018 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019
## [659] 2019 2019 2020 2020 2020 2020 2020 2020 2020 2020 2020 2020 2020 2020
## [673] 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021 2010 2010
## [687] 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2011 2011 2011 2011
## [701] 2011 2011 2011 2011 2011 2011 2011 2011 2012 2012 2012 2012 2012 2012
## [715] 2012 2012 2012 2012 2012 2012 2013 2013 2013 2013 2013 2013 2013 2013
## [729] 2013 2013 2013 2013 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014
## [743] 2014 2014 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015
## [757] 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016 2017 2017
## [771] 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2018 2018 2018 2018
## [785] 2018 2018 2018 2018 2018 2018 2018 2018 2019 2019 2019 2019 2019 2019
## [799] 2019 2019 2019 2019 2019 2019 2020 2020 2020 2020 2020 2020 2020 2020
## [813] 2020 2020 2020 2020 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021
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## [841] 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011 2012 2012
## [855] 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2013 2013 2013 2013
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## [883] 2014 2014 2014 2014 2014 2014 2015 2015 2015 2015 2015 2015 2015 2015
## [897] 2015 2015 2015 2015 2016 2016 2016 2016 2016 2016 2016 2016 2016 2016
## [911] 2016 2016 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017 2017
## [925] 2018 2018 2018 2018 2018 2018 2018 2018 2018 2018 2018 2018 2019 2019
## [939] 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2020 2020 2020 2020
## [953] 2020 2020 2020 2020 2020 2020 2020 2020 2021 2021 2021 2021 2021 2021
## [967] 2021 2021 2021 2021 2021 2021 2010 2010 2010 2010 2010 2010 2010 2010
## [981] 2010 2010 2010 2010 2011 2011 2011 2011 2011 2011 2011 2011 2011 2011
## [995] 2011 2011 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012
## [1009] 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2014 2014
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## [3445] 2020 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021 2021# gam for 2010-2021 ndvi ----
# GAM
ndvi2010_2021_gam <-
gam(
scaled_mean_ndvi ~ #scale ndvi from 0 to 1 to fit beta distribution
# fixed effects
park +
# global smooths
s(month, bs = "cc", k = 4) + #month effect
s(year, k = 8) + #year effect
ti(month, year, k = 6), #month/ year interaction
family = "betar",
#beta location scale distribution for the data
data = mean_ndvi_df,
method = 'fREML'
)summary(ndvi2010_2021_gam)##
## Family: Beta regression(55.1)
## Link function: logit
##
## Formula:
## scaled_mean_ndvi ~ park + s(month, bs = "cc", k = 4) + s(year,
## k = 8) + ti(month, year, k = 6)
##
## Parametric coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.03827 0.02571 1.488 0.13666
## parkBANF 0.09987 0.03404 2.934 0.00335 **
## parkELKI 0.40593 0.03436 11.814 < 2e-16 ***
## parkFIVE 0.45582 0.03444 13.233 < 2e-16 ***
## parkFORI 0.39645 0.03435 11.543 < 2e-16 ***
## parkFUND 0.50959 0.03455 14.751 < 2e-16 ***
## parkGBIS 0.42062 0.03438 12.233 < 2e-16 ***
## parkGLAC 0.09946 0.03404 2.921 0.00349 **
## parkIVVA 0.15227 0.03551 4.288 1.80e-05 ***
## parkJASP 0.10829 0.03405 3.181 0.00147 **
## parkKEJI 0.51878 0.03456 15.010 < 2e-16 ***
## parkKOOT 0.16160 0.03408 4.742 2.12e-06 ***
## parkKOUC 0.38077 0.03432 11.094 < 2e-16 ***
## parkNAHA 0.16692 0.03409 4.897 9.72e-07 ***
## parkNOVA 0.27996 0.03419 8.189 2.64e-16 ***
## parkPALB 0.37048 0.03431 10.799 < 2e-16 ***
## parkPEIS 0.27636 0.03419 8.084 6.26e-16 ***
## parkPELE 0.14005 0.04307 3.252 0.00115 **
## parkPRIM 0.50758 0.03454 14.695 < 2e-16 ***
## parkREVE 0.20709 0.03412 6.070 1.28e-09 ***
## parkTHIS 0.42492 0.03439 12.356 < 2e-16 ***
## parkWAPU 0.12101 0.03406 3.553 0.00038 ***
## parkWATE 0.31548 0.03423 9.216 < 2e-16 ***
## parkWOOD 0.33050 0.03425 9.649 < 2e-16 ***
## parkYOHO 0.08550 0.03404 2.512 0.01201 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df Chi.sq p-value
## s(month) 1.564 2.000 6.876 0.0123 *
## s(year) 5.105 5.985 178.393 <2e-16 ***
## ti(month,year) 2.042 2.574 1.854 0.4892
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.269 Deviance explained = 27.8%
## -REML = -4438.7 Scale est. = 1 n = 3457plot(ndvi2010_2021_gam, pages = 1)
# residuals of model 1
residuals(ndvi2010_2021_gam)## [1] -0.0133442319 1.2045573051 0.0667036472 1.6050188204 0.7856933621
## [6] 0.0808132391 -0.0901063516 -0.0484421646 0.2739720015 -0.0025367921
## [11] 1.2318332569 0.0877320642 1.5727170421 0.3080228654 0.0471721975
## [16] -0.0725158655 -0.0522099656 0.1744876770 -0.0585758896 0.4656800502
## [21] 0.0777749722 1.7788751507 0.9639607866 0.0102143461 -0.1586804737
## [26] -0.1228592824 0.0496600009 -0.1417974517 0.6924508746 -0.0752056755
## [31] 0.7332279196 -0.0894710312 -0.1086562591 -0.2582483604 -0.2312594770
## [36] -0.1771063279 -0.4231595170 1.1022283259 -0.6019318727 1.4829356826
## [41] 0.1177339926 -0.4641081760 -0.4294588052 -0.5947787650 -0.1135174062
## [46] -0.5626068716 0.7813673497 -0.7897978701 1.4366465087 0.2217954685
## [51] -0.5863555823 -0.5780453752 -0.7993393262 0.2113359267 -0.6122604132
## [56] 0.8609343424 -0.8845196044 1.5337756797 0.1947527313 -0.6830293793
## [61] -0.6456106848 -0.7994386886 -0.3130952244 -0.5987931057 0.9930023255
## [66] -0.8045722101 1.4206356841 -0.2028223379 -0.6328149168 -0.6892545044
## [71] -0.8021993153 -0.0377147538 -0.5341126450 0.1770666806 -0.7563820285
## [76] 0.8082131227 -0.3138772046 -0.5926035294 -0.5755187746 -0.7300234852
## [81] -0.4902057038 -0.4849950980 0.3568204147 -0.7225425809 0.5209508617
## [86] -0.4291097484 -0.5738548365 -0.5759440901 -0.6225513633 0.3167078452
## [91] -0.4773785106 0.9717335819 -0.6330422977 1.3910265969 -0.1987410759
## [96] -0.5210205780 -0.5433165598 -0.6869770793 -0.1012033690 -0.5139993803
## [101] 0.4820096137 -0.6823902758 0.8641432080 -0.0905807945 -0.6039430707
## [106] -0.5751335932 -0.7016390443 0.5239535265 0.1729558710 0.6716044457
## [111] 0.3394503413 0.3263669151 0.3332144922 0.7772974075 0.3248857923
## [116] 0.2673491802 0.0831803028 0.2348253923 0.8794501706 0.5843849696
## [121] 0.0420623039 1.1528866909 0.2803627640 0.2414022810 0.2360708217
## [126] 0.8282374382 0.2398632070 0.1244012595 0.0047839145 0.1812339742
## [131] 0.3812322439 1.2196954770 0.0269107397 1.3033238761 0.1940130370
## [136] 0.3060508499 0.2030415822 0.8264618076 0.1587095799 0.0893389300
## [141] 0.0723801694 0.0867578483 0.2667505571 1.3976114898 -0.1028312167
## [146] 0.7231432585 0.0318794975 0.0618728849 0.0711732574 0.9107003733
## [151] 0.1394127765 -0.0381700690 -0.0307945999 -0.0508938077 0.3517093238
## [156] 0.7894074508 -0.4888014524 0.5776783007 -0.3971938123 -0.2548622865
## [161] -0.2919354163 0.9570057576 -0.1601691523 -0.4340279855 -0.5163361009
## [166] -0.4206541013 0.2013575400 0.4561442582 -0.5183073076 0.5765331754
## [171] -0.5937714416 -0.5008974008 -0.5159008934 0.4395476853 0.1972088009
## [176] -0.5328459860 -0.3290935808 -0.5607673851 0.3249349775 0.0867645632
## [181] -0.5020752232 0.3578377781 -0.6727116630 -0.5028429223 -0.5805408013
## [186] 0.1003044116 0.0395336865 -0.5734836935 -0.3032487956 -0.5460573329
## [191] -0.4820289406 0.0882317836 -0.6950666805 0.8576905394 -0.4543500165
## [196] -0.5312431731 -0.5160089029 0.9302743609 -0.1169020174 -0.6985503077
## [201] -0.5648724480 -0.7342001546 -0.3355076885 0.2703480335 -0.6116624535
## [206] 0.8472639281 -0.4433523269 -0.5366987367 -0.5482087870 0.6843417373
## [211] 0.0017766537 -0.5969637640 -0.2757241330 -0.5324198797 -0.3212959877
## [216] -0.1431243650 -0.4758887187 0.7172500967 -0.6048386557 -0.4272221033
## [221] -0.4114490531 0.2434726938 -0.1454176124 -0.4774290146 -0.5513596072
## [226] -0.5417952874 -0.4176884065 0.1710283703 -0.5475832937 1.0457298684
## [231] -0.4295468566 -0.4729471312 -0.5892968392 0.5093966223 -0.3225064385
## [236] -0.5606713196 -0.6193194062 -0.5311228478 -0.2543513801 0.6682198472
## [241] -0.5232711948 0.4707905403 -0.6606277903 -0.5141302368 -0.4840102028
## [246] 1.1394093233 0.2015674761 -0.5115820943 -0.5433693413 -0.5623567668
## [251] 0.0691388683 0.3607679819 -0.4291469976 1.3999775948 -1.5259303279
## [256] -1.3529830183 -1.4564759219 1.5980163744 1.2447383579 -1.1963471597
## [261] -0.5925142970 -0.6933981289 -0.0586485093 0.4648849753 -1.2382889592
## [266] 3.5085638049 -1.1340984815 -1.3753739112 -1.4406834386 2.1832457496
## [271] 0.8267941839 -1.4060345660 0.1453215038 -0.8322311633 0.0352013165
## [276] 2.0568602333 -0.5909364307 2.5722008529 -1.5915406684 -1.2198195013
## [281] -1.2598143988 2.3634090703 1.0775164649 -1.1711952617 0.0190579180
## [286] -1.5263274872 -0.6294223068 1.6764496070 -1.5616941742 1.7862848409
## [291] -1.7470507665 -1.5307600064 -1.6734167836 2.0144265186 0.7066842590
## [296] -1.6214658699 0.2165404596 -1.6077499122 -0.3854316551 1.9137828539
## [301] -0.9921691402 2.3017661826 -1.4404379091 -1.4727624611 -1.6162617673
## [306] 3.8978684214 1.2514000993 -1.4578098518 -0.3996979907 -1.0747607253
## [311] 0.2061501156 0.8704362744 -0.5923768011 2.5863915911 -1.5014453682
## [316] -1.6225883665 -1.4557124693 2.9457869162 1.7606311686 -1.3927946859
## [321] 1.2774445478 -0.8478059940 0.4299857386 0.7807267127 -0.2677686559
## [326] 2.1494380420 -1.3792086663 -1.2867215546 -1.6075902949 2.7554579226
## [331] 1.9990802692 -1.0164762006 0.5579378381 -1.1874798369 -1.0701725055
## [336] 0.9185074112 -1.3668116341 2.9907794274 -1.2282282706 -1.4864551891
## [341] -1.5839255046 2.9566653499 2.2428376274 -1.5742788858 0.7142324332
## [346] -1.6889415793 -0.3772165374 0.9541707831 -1.2774042437 1.7635119159
## [351] -1.6176847721 -1.5713807425 -1.4192008626 2.6626273240 2.4640686483
## [356] -1.7248627263 1.5282555911 -1.5212372913 -0.2133939436 -0.0893292304
## [361] -0.5005887540 1.8262146384 -1.3739929190 -1.5258656041 -1.6386968795
## [366] 1.2624350857 1.1148221764 -1.6335834369 0.3541934627 -0.9932862147
## [371] -0.0522871224 0.6641214026 -1.0870898480 3.4873874226 -1.4586295022
## [376] -1.5460020550 -1.4634833184 2.4859011099 1.4899095039 -1.6667789556
## [381] 0.3405564139 -1.4138635088 -0.4494665988 1.2447155017 -0.3694778052
## [386] 1.6530278331 -1.5827476146 -1.4993894371 -1.5671204087 2.5630635089
## [391] 2.5186569061 -1.4128638212 0.0150228026 -0.7657819456 0.4354271410
## [396] 1.0510273771 -0.3762914838 0.6194767382 -1.4208527232 -1.0284793464
## [401] -1.3671830641 0.6834504663 -0.1800704899 -0.2116017429 0.1786229957
## [406] -1.1390306578 0.0281056282 -0.5449732920 -0.2435529847 0.3903295363
## [411] -1.5241727548 -1.1349839265 -1.3734994377 0.7099187737 0.3346687758
## [416] -1.0625472498 -0.6631020977 -0.7741222466 -0.2642456767 -0.1375771748
## [421] -0.3354294161 0.5203301917 -1.6452450697 -1.0953483670 -1.3784068851
## [426] 0.7369904101 0.6083015987 -0.9401270588 -0.2780199870 -1.4880130038
## [431] -0.9030398598 0.5317648203 -1.1749855547 0.4787399173 -1.7438553446
## [436] -1.5469056578 -1.6144507787 0.8482515395 -0.0628342266 -1.1622979618
## [441] 0.0444584949 -1.4264733025 -0.4852066540 0.4518432547 -0.5176332685
## [446] 1.8705792768 -1.0889524202 -1.2236332540 -1.3252708241 2.3541699582
## [451] 2.4490875891 -1.1046427403 0.8495190787 -1.5228007910 -0.4627502702
## [456] 1.1192655781 -0.2907623932 1.5769072023 -1.5084626793 -1.3538334185
## [461] -1.2111829597 2.7637573464 1.8764618232 -1.1858606561 1.1122802158
## [466] -0.6651788150 0.0068170708 1.0943702702 -0.0729383037 2.0477880101
## [471] -1.6959625940 -1.2379114160 -1.7113256177 2.7170730763 2.8455679863
## [476] -0.8368137344 1.7227692224 -0.2129442674 0.1710921863 1.7379502035
## [481] -0.0654746862 1.6878887012 -1.5556529795 -1.3692856658 -1.4871014246
## [486] 2.3893640466 1.6122410000 -0.6133585065 0.3339877708 -1.5229327528
## [491] 0.2491216145 1.8708924728 -1.0956529973 1.8243433690 -1.1381028101
## [496] -1.2245686532 -1.4432846691 2.6729937253 1.5731092860 -0.7295925022
## [501] 1.4967165313 -1.5211223817 -0.7442060725 1.3548534912 -0.1904577664
## [506] 3.4361511138 -1.3530054126 -1.4128895521 -1.2296483950 1.9861506220
## [511] 1.7713275705 -1.2279626995 0.3208515028 -1.3766898038 0.3664753113
## [516] 0.6867372733 1.1348575262 2.1537694275 -1.3313227145 -1.1048480183
## [521] -1.3907107516 2.6378732980 3.5246054533 -0.9833690716 1.2600573287
## [526] -0.8617559164 0.0152926916 1.2295242710 0.1208675400 1.3514454621
## [531] -1.6930256048 -1.0683673682 -1.0848329599 1.2249554818 1.4994781192
## [536] -0.2186982242 0.8292558364 -0.8789018444 -0.3385097658 1.1648889416
## [541] -0.6628390551 1.3186637189 -1.0694035606 -1.2679959336 -1.0469272040
## [546] 0.7410996655 0.8493122539 -0.8054526057 0.3734721360 -0.6160005165
## [551] -0.2859221648 -0.1823034260 -0.9706854472 0.1431073992 -1.1034188862
## [556] -1.1929031918 -1.0457515591 0.3732796251 0.2824869696 -1.0644959685
## [561] -0.8399921202 -0.9990068439 -0.7463393072 1.2589185487 -0.8330172266
## [566] 0.4142882296 -1.2414126080 -1.1029267734 -1.3098781350 1.2231163517
## [571] 0.9463757320 -0.9816316061 0.1766026232 -0.5358492841 -0.2571633696
## [576] 0.5353716227 -1.0266340074 0.4383349602 -1.2480180976 -1.2417737173
## [581] -1.1928024883 0.8882965667 0.4353059201 -1.3235910904 -0.5246069041
## [586] -0.7046158238 -0.3983401962 -0.0583656638 -0.8779439274 2.0691041768
## [591] -0.8300250776 -0.8640867566 -0.4652542157 2.0814027203 1.8200795331
## [596] -0.9064581017 -0.1785450886 -0.9584803154 0.6149407564 2.3760348230
## [601] -1.1456841586 2.0465709296 -0.5984140062 -0.9824333435 -0.7941982664
## [606] 1.5528747068 1.2725717547 -1.0185792595 -0.2973873528 -0.8629403065
## [611] 0.3371076619 2.3079413197 -0.4358307727 2.2511178494 -1.1760651492
## [616] -0.8742088543 -0.9249364581 1.2812103278 0.7377892667 -0.8440793099
## [621] 0.2943695384 -0.8840173548 0.4323610584 1.4080617302 -1.1485328198
## [626] 1.9239172444 -0.8269241826 -0.9761384397 -0.9217971804 2.8788920024
## [631] 1.6356576220 -0.9713450317 -0.1626902130 0.0251936503 0.5697339464
## [636] 0.9409901142 -0.8345872363 2.1330426567 -0.7989296249 -0.7662523820
## [641] -1.0520064866 2.6733896300 1.3794643858 -1.1373835027 0.1542410750
## [646] -0.7028722961 -0.2950771350 1.8930488355 -0.9856002733 1.9412257108
## [651] -0.6030375052 -0.6534185396 -1.0542511897 2.1600007464 0.7857463403
## [656] -1.0279606405 -0.6400144343 -0.6690197185 0.6882422745 1.1125925871
## [661] -0.7919085605 2.1327603568 -1.1345299566 -0.7877253073 -1.0392927155
## [666] 1.6580791502 1.4434083400 -0.8293273517 0.2109003407 -0.6519231641
## [671] 0.0862142926 1.4565378852 -1.0409495214 2.1817209755 -0.7957794951
## [676] -0.9697422493 -1.1169711730 1.1777275349 1.5687563286 -1.0687223372
## [681] 0.5010524063 -0.4742852077 0.1475429635 0.0802847847 -0.6937015054
## [686] 0.7905766273 -1.4382653508 -1.2601307950 -1.3296890665 1.0256067122
## [691] 0.0526321620 -0.8058573425 0.0025509713 -0.6379688349 -0.2586298090
## [696] -0.0822603757 -0.7330749774 0.1975740797 -0.8951794766 -1.2564774966
## [701] -1.3888636012 0.3933614482 0.1322071250 -1.0258887144 -0.8200933535
## [706] -0.5369444561 -0.5649049937 0.8931407523 -0.5282745578 0.9208028845
## [711] -0.8643680454 -1.0441083702 -0.9728716484 1.4861452661 0.3982886949
## [716] -0.6936253651 0.2064419110 -0.3471242887 -0.1174713849 0.7361818489
## [721] -0.3347697991 1.4856183010 -1.4951547268 -1.2220128060 -0.8734369807
## [726] 0.5096589166 0.2565633273 -1.1980507328 -0.0501089666 -0.9207139272
## [731] 0.1330035640 0.1147847034 -1.0958662369 1.4443559248 -0.4950367467
## [736] -0.5030349422 -0.8232322395 1.7449663962 1.2081084409 -0.4401313804
## [741] -0.1519799613 -0.8651110744 -0.1912519210 1.5474210905 -0.9265789831
## [746] 2.2074555354 -0.6178334529 -0.8441960035 -0.4274146018 0.9564033219
## [751] 0.2072581190 -0.9749326458 0.4430699288 -0.9226954485 0.7077518650
## [756] 1.8212585532 0.2658984628 0.6230810475 -0.6965306605 -0.7371232620
## [761] -0.2450353394 1.2664144147 0.7737031813 -0.7937566973 -0.6110694943
## [766] -0.7471623717 0.2572495049 1.2505028973 -1.0280358539 1.6098016963
## [771] -0.6026954523 -0.6425309208 -0.5925961914 1.2797687151 0.8809419654
## [776] -0.5332540789 -0.2044226824 0.0368117218 1.0247928333 1.1785386237
## [781] -0.6571774115 1.5768661100 -0.0651120063 -1.1074303843 -0.5468811040
## [786] 2.3802161446 0.9110443299 -1.2103203829 0.8090686191 -0.6152730241
## [791] -0.3544242771 1.4914149070 -1.0940290521 1.8723254154 -0.4808790600
## [796] 0.0118558264 -0.6153678324 1.8123973793 0.9411087262 -0.2878322413
## [801] -0.7617772247 -0.7753996735 0.4252264414 1.3002565830 -0.1663842785
## [806] 1.8171697589 -0.9426785638 -0.7708410204 -0.9507599412 0.9628611311
## [811] 1.3863919067 -0.8721893149 0.0843934379 -0.4818608575 0.0398990314
## [816] 1.4682906959 -0.1917178018 1.6519048163 0.0282100390 -0.8580277045
## [821] -0.8556631715 0.0821126807 0.7569098199 -0.3863929902 -0.1949088071
## [826] -0.0624833748 -0.0635215165 0.7838443815 0.4379089033 0.7398455935
## [831] -1.4066906565 -1.1660230969 -1.2534422769 1.7425070976 0.8831280502
## [836] -0.4261995689 1.2181449994 -0.6434864549 0.2178964233 -0.2798031017
## [841] -0.2487757331 1.1566495931 -1.1346528846 -1.1687022753 -1.3096539515
## [846] 2.1963474718 1.2484038442 -1.0865761316 -0.1444025079 -0.5975413756
## [851] -0.0934859920 0.4842272639 0.1053047562 1.1171376951 -1.4403176043
## [856] -1.2116965027 -1.3701381842 2.1861168471 1.2765389870 -0.7015061466
## [861] 0.6045268425 -1.1432622364 -0.7161480265 1.1060483902 -0.7753456159
## [866] 1.6755120616 -1.5856472471 -1.4391548114 -1.4920079150 1.4305389415
## [871] 1.0598431149 -1.3075069945 0.6994408033 -1.2832358999 -0.1934095705
## [876] 1.2265814471 -1.1473648224 1.4937795210 -0.9072502323 -1.2788815534
## [881] -1.3259307567 2.2522272313 1.6620749689 -1.2832373433 0.2530868096
## [886] -1.1736828673 -0.4383918203 0.9799415690 -0.4487597058 1.0496248658
## [891] -1.4930222617 -1.3043859157 -1.2603891748 2.6943851260 1.7675282480
## [896] -1.4289643073 0.5130453328 -0.4045581308 -0.1363221154 1.3869917514
## [901] 0.4859737502 2.1329100451 -1.4156298988 -1.3605013695 -1.4677774178
## [906] 2.3934851828 2.2268232570 -1.0940114888 1.0726442102 -0.4281815657
## [911] -0.0446419124 1.5275095048 -0.2021865349 1.4129328618 -1.2219474758
## [916] -1.4795401384 -1.4206835224 1.6333087540 1.4259433822 -1.2304987140
## [921] 0.1353031557 -1.1974836864 0.0943705073 1.1324736357 -0.8231211308
## [926] 1.3498689780 -1.3104941162 -1.5192921322 -1.4507348851 2.0667785562
## [931] 1.0918882403 -1.2060922803 0.6492423832 -1.1485229466 -1.0390724863
## [936] 0.9788287053 -1.0325094200 2.5212320674 -1.3707932056 -1.4495858865
## [941] -1.2421383052 2.4530547323 1.4308498242 -1.3905967001 -0.1652740558
## [946] -0.9500787816 0.3450946553 0.8652368585 0.1014117595 0.9039725282
## [951] -0.8975085726 -1.3130973247 -1.4584246723 1.4161228243 2.5995551884
## [956] -1.2017616539 0.9524089851 -0.5105258449 -0.6010552392 0.5675057310
## [961] 0.1140401400 2.0155919890 -1.2101275541 -1.3010205694 -1.3304074473
## [966] 0.1043749862 1.3951691506 -0.9857125860 0.8720864293 -0.8760025737
## [971] -0.6362825409 0.7670959213 0.0688363824 0.9577822807 0.0954229074
## [976] 0.2000207229 0.1254122539 1.0708040648 0.3482431558 0.1743690353
## [981] 0.0864972740 0.0471814719 0.7595353557 0.7244030570 0.0580586712
## [986] 1.4353993437 0.0736238490 0.1804625341 0.1064647402 0.6867490186
## [991] 0.1963632901 0.0604831264 0.0152929162 -0.0042391231 0.2219733639
## [996] 1.5277092161 -0.0241936047 1.7216494169 -0.0177018436 0.1167742974
## [1001] 0.0579639431 0.7820804226 0.0480772732 0.0169104608 0.0241215198
## [1006] -0.0384973876 0.4538934240 1.7657366530 -0.0729294919 0.9077660081
## [1011] -0.0487353621 -0.0092596625 -0.0868640814 1.1379729741 0.1450365471
## [1016] -0.0546641378 -0.0738580379 -0.1709500912 0.3831499434 0.8448994172
## [1021] -0.4896304459 1.0620713159 -0.5311732697 -0.3400801642 -0.4064283909
## [1026] 1.2584071868 -0.0654769708 -0.4854502052 -0.4869344414 -0.4652363229
## [1031] -0.0479385251 1.0049856794 -0.5878680791 1.2266159760 -0.7845086563
## [1036] -0.5655512622 -0.6845041487 0.7297339771 0.2786577545 -0.6202213345
## [1041] -0.3924014006 -0.7040837605 0.1991293141 0.2559631119 -0.7093934153
## [1046] 0.7858964956 -0.7994268741 -0.6512160001 -0.7409870573 0.0952159913
## [1051] 0.0215770098 -0.7025423375 -0.4900419108 -0.8177640931 -0.5174839531
## [1056] 0.4057857056 -0.6789467448 1.3047720670 -0.7054814788 -0.5820057468
## [1061] -0.6417484027 1.1778267403 -0.1877746731 -0.7331083414 -0.5784216842
## [1066] -0.7927286917 -0.2285528042 0.6143296935 -0.6264988524 1.2908984887
## [1071] -0.6866478569 -0.5953378264 -0.6861595132 1.1666749313 -0.0669193977
## [1076] -0.6076304142 -0.3594623882 -0.7399607175 -0.2175482841 0.0117296631
## [1081] -0.5143439754 0.8306887128 -0.7138100304 -0.4805777880 -0.6032642556
## [1086] 0.3069419900 -0.0596990903 -0.5106160170 -0.5072617246 -0.6098411237
## [1091] -0.4232303740 0.1749210421 -0.5535704467 1.2796802529 -0.6339044996
## [1096] -0.5326430009 -0.6777592814 0.4747343929 -0.4101471365 -0.5813915349
## [1101] -0.6141684625 -0.6247319611 -0.2469782683 1.0525198390 -0.5824904000
## [1106] 0.5769050028 -0.7202826551 -0.5752165796 -0.6620154979 1.5853029596
## [1111] 0.1332719750 -0.6063867295 -0.5796710731 -0.7304737165 -0.3281569039
## [1116] 0.2354830131 -0.4666825859 0.8476855245 -0.3887250950 1.3544044913
## [1121] 1.3152998797 -0.3673917297 -0.1329795056 -0.6580680338 -0.4397570915
## [1126] 0.3632404328 -0.4597884753 1.4685301200 -0.4257826725 1.2381853066
## [1131] 1.0382628019 -0.3993934874 -0.1544961161 -0.6861334644 -0.4474480089
## [1136] 0.2232557524 -0.5152645344 1.2046152415 -0.5178194246 1.5907115010
## [1141] 1.4594686185 -0.4153551708 -0.3663671361 -0.6656865413 -0.1521600435
## [1146] 0.4806361781 -0.6094429487 1.2777000041 -0.5880755386 1.4215362355
## [1151] 0.8295689015 -0.5746543912 -0.6626336668 -0.7205477577 -0.5479434434
## [1156] 0.1341140734 -0.9620697865 1.6539171427 -1.0506197904 2.1687506992
## [1161] 1.8603526537 -0.9921456615 -0.5098168493 -1.2813547797 -1.0417804079
## [1166] 0.3078004443 -1.1492659970 0.8401634769 -1.2732785191 1.9954494571
## [1171] 1.7329378201 -1.1682766677 0.2329746783 -1.4456068287 -1.2671716265
## [1176] -0.1942341236 -1.2182183175 1.1390385211 -1.3246765179 1.9764028117
## [1181] 0.9144393041 -1.2495262180 -0.5307633450 -1.4275375226 -0.3856439828
## [1186] 0.3434272017 -1.1405966782 1.3864393862 -1.2554747171 2.7762136289
## [1191] 2.2003515035 -1.1323621405 -0.3637951254 -1.4427535134 -1.0359513260
## [1196] 0.3809651549 -1.1024747562 1.2921516881 -1.1376345411 2.0013344068
## [1201] 0.8192050920 -1.1448471591 -0.8453305326 -1.4397701106 -1.1019983771
## [1206] 0.5198602554 -1.0421346400 0.4403034984 -1.1965909301 2.3099222099
## [1211] 2.1392594035 -1.0977952626 -0.4587075409 -1.1122992402 -0.5795573024
## [1216] 0.7478567370 -0.8985799366 1.3778164714 -1.1218123354 1.3819146109
## [1221] 1.9084523033 -1.0014606184 0.0737058046 -1.2523544655 -0.8096719677
## [1226] 0.1649916033 -0.9837923757 1.1994490946 -1.2118057942 1.8276909740
## [1231] 2.0009921587 -1.1241670960 -0.4451868435 -1.4406880860 -1.1200129681
## [1236] 0.5471341217 0.1914555089 0.5232618163 0.3147238246 0.3192158587
## [1241] 0.2658355413 0.9209540624 0.3333691265 0.2042540752 0.0256472010
## [1246] 0.1563708734 0.7324218417 0.4882047887 0.0489350843 0.8978730572
## [1251] 0.1659215340 0.2063149437 0.1757926475 0.6089576048 0.2332404002
## [1256] 0.0783035431 0.0456688377 0.1080749661 0.3261361432 1.1443430777
## [1261] -0.0250492362 1.1835444399 0.1526794280 0.2591254294 0.1288357642
## [1266] 0.7466991798 0.1606376585 0.0664693814 0.1039246723 0.0097007539
## [1271] 0.1621648441 1.4864362925 -0.1260796719 0.6872392996 -0.0474036453
## [1276] 0.0058486843 0.0064410340 0.7700853291 0.1528825572 -0.0773373743
## [1281] -0.0082550304 -0.0753157107 0.3551592045 1.0997557325 -0.4613597476
## [1286] 0.8243504670 -0.2998735688 -0.1692907814 -0.2385228068 1.1083294268
## [1291] -0.0580521785 -0.3994020717 -0.4296463774 -0.4274957639 0.1849829174
## [1296] 0.6702197025 -0.4909039352 0.5650419254 -0.4912986464 -0.5515226702
## [1301] -0.5415337268 0.5234200875 0.2015738977 -0.5063872923 -0.3695760293
## [1306] -0.5490600721 0.2220658939 -0.0976156668 -0.4110014931 0.4147807402
## [1311] -0.5338843044 -0.4137278949 -0.3691963328 -0.0507063971 0.0272797979
## [1316] -0.5620286811 -0.1119567240 -0.5958266278 -0.3727794093 0.3372226802
## [1321] -0.6644482332 0.7710153668 -0.3821188271 -0.4527220121 -0.4453354061
## [1326] 0.8203707811 -0.1273589532 -0.6416764810 -0.4890162073 -0.6997177943
## [1331] -0.2906083948 0.1160623259 -0.5294166713 0.7856087656 -0.4057209550
## [1336] -0.5099131712 -0.4672277040 0.6482863209 0.0784775544 -0.5247886265
## [1341] -0.1155356377 -0.5869986877 -0.1669270926 -0.1447889661 -0.3794599280
## [1346] 0.5130530701 -0.5523030214 -0.4160154387 -0.3769944835 0.0870231093
## [1351] -0.2075199636 -0.3382799010 -0.3955017339 -0.5609231664 -0.4092392211
## [1356] 0.1924332906 -0.5075142168 0.9695173798 -0.3812417446 -0.4633877892
## [1361] -0.5884320622 0.2877923272 -0.3337951933 -0.5258814800 -0.5544762383
## [1366] -0.5346036449 -0.2310639197 0.6370478737 -0.4439153027 0.4028599743
## [1371] -0.6379682517 -0.4941197565 -0.4111920087 0.9720435940 0.2813453404
## [1376] -0.5102879502 -0.5124036565 -0.4877832297 -0.1679802806 0.0351218859
## [1381] -0.3436144789 0.4893708549 -1.4781085570 -1.6256398260 -1.5986740838
## [1386] 1.3257687367 0.2474425763 -0.4035174769 0.8004797798 -0.8933696116
## [1391] -0.4259807371 0.4344869855 -0.2096618889 0.1839304337 -0.8537991429
## [1396] -1.3932536787 -1.3182928071 0.5301683730 0.1410892026 -0.6048595748
## [1401] -0.9570359056 -0.2820449515 -0.5159314468 1.2428742683 -0.3753087824
## [1406] 0.9954650452 -1.1687171812 -0.9737821979 -1.0928756528 1.4147746498
## [1411] 0.4456306757 -0.3034076154 -0.0487251385 -0.2573556677 -0.1333857260
## [1416] 0.5240042536 -0.1956909535 1.1636377484 -1.9777120997 -1.3021668298
## [1421] -1.3091097343 0.2630794408 0.0468703026 -1.1311224543 -0.2353423060
## [1426] -1.2817588239 0.4805390924 0.3738077593 -0.4004478863 0.9946213533
## [1431] -0.5085470902 -1.1021091196 -1.1625987501 1.6883110331 1.0282090764
## [1436] -0.7912972741 -0.4297185160 -0.7155593013 -0.4795769644 1.9366246223
## [1441] -1.1681520004 1.7411747191 -0.5642091474 -1.3470386648 -0.9707849734
## [1446] 1.2129709516 0.7512062437 -1.4136946271 0.2801427046 -0.4648008526
## [1451] 0.6939865024 1.8012658715 0.3919050758 1.4562995180 -1.1458375835
## [1456] -0.6276731780 -0.8746483856 1.5550650676 0.9890937408 -0.2215241679
## [1461] -0.5290743121 -0.7153013920 0.5259552342 1.2706179409 -0.1888934562
## [1466] 1.7979942252 -1.0385023352 -1.0543815543 -1.0177578567 0.9097370813
## [1471] 0.5271624098 -1.0973611385 -0.0699032234 -0.4573892346 1.4924297441
## [1476] 0.5652458664 -0.4769162876 1.2502545993 -0.8070142852 -1.0885311878
## [1481] -1.1673746477 1.7145819628 1.3918854130 -1.1392164595 1.0095136047
## [1486] -0.3228176713 -0.6009585456 1.5965713953 -0.6645559241 2.1945943023
## [1491] -0.8602142480 -0.4235766698 -0.4943232211 2.0540846126 0.3755619691
## [1496] -0.3001996331 -0.5069406933 -0.3798282361 0.3194787613 1.8037671555
## [1501] -0.0600854274 1.4813417220 -0.8948309291 -0.6586191058 -0.9924954464
## [1506] 1.0000357781 0.8631671793 -0.2213754160 0.5329003556 -0.4823137338
## [1511] 0.2618720147 1.1765317004 0.0038614992 1.3195472443 -0.4930676700
## [1516] -1.0826715561 -0.8309974414 0.2206157160 1.8154448586 0.1290585393
## [1521] -0.0808283370 -0.1732266712 0.4554687765 1.1282649699 -0.0648870567
## [1526] 0.8595401998 0.1028818201 0.1300947542 0.1124945745 0.7740408112
## [1531] 0.1869259807 0.0589312209 -0.1051496534 0.0441086618 0.7397859950
## [1536] 0.5246349238 -0.1954893348 1.5200950139 0.1137836332 0.0527055936
## [1541] 0.0273162949 0.5865732897 0.0227992026 -0.1273149151 -0.2051951295
## [1546] -0.0558862197 0.1912489079 1.4843633561 -0.2323051172 1.7076868442
## [1551] -0.0421854736 0.0318121032 -0.0460192167 0.8776643188 -0.0827527275
## [1556] -0.2287543622 -0.0833524938 -0.1792415806 0.1865925509 1.6218828674
## [1561] -0.3104769530 0.7604106689 -0.0813234635 -0.1449726041 -0.0720739948
## [1566] 1.0800787670 0.0493538190 -0.2625069008 -0.1851778579 -0.2181619368
## [1571] 0.4493230008 0.6831378590 -0.5436903144 1.0186726138 -0.5046118146
## [1576] -0.3398308026 -0.5028288003 1.4233986147 -0.0263186236 -0.5538979410
## [1581] -0.4485488455 -0.3987341123 0.0789654791 0.7301851097 -0.4777363050
## [1586] 0.8309031935 -0.7738817412 -0.5392628884 -0.6747068351 0.7659499744
## [1591] 0.4674042031 -0.5805494637 -0.1070800940 -0.6954701987 0.4497773215
## [1596] 0.2190597473 -0.5330135544 0.8193546664 -0.7741651392 -0.6013989039
## [1601] -0.8022579708 0.1445629109 0.1470595489 -0.7187938417 -0.1881579167
## [1606] -0.6562438083 -0.5572130736 0.2533322236 -0.7516364997 1.4608947032
## [1611] -0.6370664587 -0.6217372605 -0.5944412353 1.7163158730 -0.0373382848
## [1616] -0.8008145564 -0.4454947561 -0.8650321024 -0.2138390141 0.4610692397
## [1621] -0.6210396993 1.0263261162 -0.6008387055 -0.6477170905 -0.7491996029
## [1626] 1.2170514051 0.1061292513 -0.6988333936 -0.1297747193 -0.7625282964
## [1631] -0.1062260368 -0.0646674472 -0.5228772574 1.1165213918 -0.7463269106
## [1636] -0.4716899233 -0.5463538904 0.3771716395 0.1130209382 -0.4757148158
## [1641] -0.4181697425 -0.5903870958 -0.2834628902 0.1310792209 -0.5762811923
## [1646] 1.5192069428 -0.5779275364 -0.5632483106 -0.7829009408 0.8305210679
## [1651] -0.2998718669 -0.6259349928 -0.6360987519 -0.5993914648 -0.3313690726
## [1656] 0.9596539423 -0.5402725300 0.7449711375 -0.7515697107 -0.6180514884
## [1661] -0.6050588077 1.8878599040 0.5568356322 -0.5761301710 -0.5118985221
## [1666] -0.6661758657 0.0714569758 0.5318485698 -0.6260827241 0.7037062309
## [1671] -0.8009764875 -1.1365402445 -1.0089851967 0.4754633392 -0.0217316185
## [1676] -1.0866983658 -0.0575621236 -0.7288637412 -0.5851002408 -0.2631580861
## [1681] -0.8317236362 0.1838489275 -0.5412485761 -1.1884011710 -1.2307065270
## [1686] 0.0926655065 -0.1437641873 -1.2426091904 -0.7415259460 -0.2246888090
## [1691] -0.5022024482 0.4579509914 -0.5430606859 0.1839171287 -0.8285015092
## [1696] -1.1876087612 -1.0739712711 0.7156143911 0.5723604375 -0.8940174218
## [1701] -0.3772658671 -0.2510220062 -0.2264174474 0.0808299874 -0.6831054574
## [1706] 0.4724278268 -1.2754877870 -1.2862577263 -1.3179272678 0.4736965311
## [1711] -0.3847285470 -1.3994350308 -0.3800643321 -0.5467829969 0.1331081058
## [1716] -0.0490818712 -1.0434666810 1.4074471214 -0.5394960578 -0.9100643499
## [1721] -0.8990921524 1.9605539295 1.5544380146 -1.0098706599 0.3475692297
## [1726] -0.7181590199 0.3643616587 1.8443707104 -1.2655872078 2.1133518586
## [1731] -0.7645921943 -1.0298072177 -0.6309303897 1.1679612833 0.6064882382
## [1736] -1.2362409596 1.0118368848 -0.4230665810 0.7254009583 1.9205028298
## [1741] 0.5966829810 1.1156248725 -0.8164189800 -1.0196732867 -0.9219085204
## [1746] 1.1975091835 0.6432257462 -0.9756890296 -0.2133538401 -0.8012324182
## [1751] 0.5713363937 1.6242062362 -0.9073096425 2.0440613008 -0.8511235982
## [1756] -1.1528923645 -1.1196563386 2.4787412711 1.1641044666 -1.1012303783
## [1761] 0.0151894028 0.0706429291 0.8846638401 1.6101916657 -1.2558300371
## [1766] 1.3987808684 -0.8690263633 -1.1957960776 -0.8720939725 2.6537965884
## [1771] 0.5677732513 -1.4207487189 1.5036238061 -0.8738429758 0.0164442614
## [1776] 1.6274037349 -0.8747303538 2.0161818726 -0.0308358105 -0.9422037521
## [1781] -1.1323613755 1.4431111150 1.2104264822 -1.1766050820 0.0889752740
## [1786] -0.2709012767 0.3768359005 1.5741982947 -0.3225693222 2.7713901700
## [1791] -0.6017115379 -0.9758616814 -0.9916278133 1.2598158105 1.8227749883
## [1796] -1.1822148332 0.7996474523 -0.3427484886 0.6566995659 1.4080317718
## [1801] -0.2424132529 2.0447237498 0.1567244828 -1.0228236505 -1.0490199134
## [1806] 0.8061962643 1.1686497625 -0.8941982481 0.8934067020 0.0003083619
## [1811] 0.1758500266 1.0281213452 -0.1605339491 0.4585341793 -0.5657172539
## [1816] -0.2480102369 -0.3592658087 1.0139232711 0.5448895985 -0.2569917005
## [1821] 0.5037440420 -0.3158713384 -0.1366312491 0.4226552617 -0.3940255893
## [1826] 0.8133195180 -0.4695747703 -0.2493823077 -0.3723883385 0.6341395009
## [1831] 0.2994765772 -0.2952261079 0.1597120592 -0.3755756328 -0.0880603545
## [1836] 0.4505410300 -0.4274951809 0.9009985087 -0.6576999078 -0.2011757461
## [1841] -0.3875539103 1.3191867613 0.3490208680 -0.3440558979 -0.1030859816
## [1846] -0.4735200809 0.0151709752 0.9330740154 -0.5488930036 0.9507192928
## [1851] -0.6789465001 -0.4629710204 -0.5606155888 0.9170024632 0.7392079445
## [1856] -0.4405705203 -0.1830344790 -0.4774853350 0.1844004722 0.5212545308
## [1861] -0.5593556460 1.7700571055 -1.0261613354 -0.3616939992 -0.7767365335
## [1866] 1.8453615947 1.2137433433 -0.3435075007 -0.0601040595 -0.7237537813
## [1871] -0.2525507174 0.8759302920 -0.6737855403 1.0802726355 -1.1909096742
## [1876] -0.7132757247 -0.8366072770 0.6622875901 1.1904511528 -0.6526946873
## [1881] 0.9844320223 -0.8474944163 -0.0561082396 -0.1033124437 -0.7792162227
## [1886] 1.3091946507 -1.1120994029 -0.7339157473 -0.9623608982 1.1537941884
## [1891] 1.4209341422 -0.8355672766 0.2135631916 -0.6581708788 -0.3048243117
## [1896] 0.8416296630 -0.6943004068 2.0915786454 -0.9067094853 -0.6758918019
## [1901] -0.8317024485 0.9710962652 0.6102620378 -0.7064327424 0.1095961182
## [1906] -0.7408742688 -0.1170314399 1.0115225554 -0.6275756314 1.0732351161
## [1911] -1.0282823170 -0.6090709738 -1.0172473025 2.1530008147 0.6525778079
## [1916] -0.5871770663 0.5263143546 -0.7061587528 0.1265684154 1.5490499234
## [1921] -0.4195545091 0.7259217512 -1.1473160833 -0.5492279305 -0.9722671859
## [1926] 1.2011993434 0.6837680276 -0.4286781992 0.2397921452 -0.8673390325
## [1931] -0.5443556819 0.9753129536 -0.6871368673 0.4455804159 -1.0372475289
## [1936] -0.6460641981 -0.9870296260 0.8626784662 0.5689478218 -0.6595383930
## [1941] -0.2259497159 -0.8486103239 0.2240188191 0.9528850750 -0.6768409322
## [1946] 0.9228725243 -1.1152588251 -0.6155194522 -0.9767617959 1.5172757087
## [1951] 1.1796047349 -0.6733733072 -0.4361806646 -0.8176280263 0.0064919707
## [1956] 0.7524781478 -0.4157953596 0.5800370089 -0.4743834349 -0.6210289349
## [1961] -0.4004266106 0.5730085532 0.9748192606 -0.6148820874 -0.3185192603
## [1966] 0.0093854288 0.1517596021 0.0513936799 -0.1918772784 0.3781998907
## [1971] -0.2666616770 -0.6620987174 -0.4968633537 0.4131928582 -0.2852695070
## [1976] -0.5719310318 0.1016769639 -0.1344938591 -0.4672358436 0.6159661015
## [1981] -0.0983454063 0.4630740995 -0.2771033522 -0.5486256069 -0.4777126320
## [1986] 0.8538593745 0.7802212670 -0.5575052618 0.1124029446 -0.0840502382
## [1991] -0.0468528309 1.1137655177 -0.3030986236 0.4315438493 -0.6750716238
## [1996] -0.7990321631 -0.4994458212 0.9558128242 0.0805157316 -0.8832889637
## [2001] 0.1546917791 -0.6611609349 0.0373552753 0.1572190429 -0.5697549672
## [2006] 0.0612509933 0.2388000480 -0.7388366986 -0.7292852493 2.5526992551
## [2011] 0.7729959733 -0.8792247732 0.3290364174 0.3036108675 0.5058999204
## [2016] 1.5112583325 -1.0527057803 1.2775209772 -0.2321657677 -0.7222235495
## [2021] -0.5898331206 0.1737640845 0.8011659648 -1.0204679007 0.0380725269
## [2026] 0.0662918149 0.2741610240 0.5099055621 -0.4257424793 0.5521504585
## [2031] -0.9684085141 -0.7601330874 -0.8812329933 0.7532128095 0.4605651762
## [2036] -0.7340575214 -0.1479346974 -0.7128660232 0.7701148959 0.3980928949
## [2041] -1.2119742957 1.2469448392 -0.7405784336 -1.0094225116 -0.8987577613
## [2046] 1.5039654843 0.5360416964 -1.0745850017 -0.1936288848 0.4098993427
## [2051] 0.7396869672 0.3706177508 -0.2676945068 1.3025791069 -0.6429680839
## [2056] 0.0107726127 -0.6707316718 1.4393472324 0.0231953985 -1.1965725567
## [2061] 0.4539570590 -0.1759892116 0.0205382806 0.7153710420 -0.4642574843
## [2066] 0.7680432407 -0.6322810759 -0.6822372957 -0.7854397193 0.4453683355
## [2071] 0.2018466927 -0.5500958162 -0.4817350965 0.0410072341 0.2148896083
## [2076] 0.4821952463 -0.9521150448 2.2533771388 -0.2803712046 -0.8471904067
## [2081] -0.9339696828 1.8403296124 0.1125642483 -1.0968533810 -0.3120532623
## [2086] 0.1726495187 0.6038678280 1.4975319530 -0.8315398822 0.7899341791
## [2091] -0.4472378336 -0.9677239113 -0.7322808396 0.8476433459 1.2680451213
## [2096] -0.9833988651 -0.0896222881 -0.0539159918 -0.0682477685 0.9985209565
## [2101] -0.0310752831 0.6575136398 -1.3099482032 -0.8790058775 -1.0182726798
## [2106] 0.9467160969 0.7141461913 -0.7500260944 0.0002494599 -0.8986107136
## [2111] 0.5875396272 -0.4618043880 -0.6596049961 2.1691949750 -1.1500114905
## [2116] -0.8362539796 -1.2507833263 1.1816920092 0.5837168985 -0.8363858354
## [2121] 0.7175394465 -0.9319167320 0.2034670489 1.9466373786 -0.6423797804
## [2126] 1.3572009445 -1.4111630304 -0.7009343375 -0.9828539688 1.6648432236
## [2131] 0.7138652786 -0.8386788609 0.2724310088 -1.3220403050 -0.9270920168
## [2136] 1.2595777071 -1.1356817125 1.4290563454 -1.3652153709 -1.1659418730
## [2141] -1.3443656933 1.1459347574 -0.0685559215 -0.9514210055 0.1756169741
## [2146] -1.3055666686 -0.4151409889 1.7724909336 -1.0455230225 1.5834100456
## [2151] -1.1613063481 -0.7410419278 -0.7813475361 2.5370210130 0.3367547262
## [2156] -0.7585720013 -0.1545385180 -1.0571847260 0.6608948413 1.1418688565
## [2161] -0.2434627020 1.5047543142 -0.9841690840 -0.9168117918 -0.9134365000
## [2166] 1.3078569688 0.9649525383 -0.8749133718 1.3083185170 -0.7690541585
## [2171] 0.6157924690 0.4677802828 0.0453731530 1.1293726081 -0.8681863825
## [2176] -1.0092215682 -1.0463934025 1.1178526476 1.7932326976 -1.1954906483
## [2181] 0.6909285030 -0.2622567263 -1.3639002725 0.4220128446 -0.6498442850
## [2186] 2.5069876765 -0.6589254362 -0.7932219050 -0.7131416756 2.4330379724
## [2191] 0.4178504634 -1.0645623411 0.5556342654 -1.0440940119 -0.2142249702
## [2196] 1.2973128796 -0.5139089359 1.1059574906 -0.8975844418 -0.6901796846
## [2201] -1.0020315128 1.2986292185 1.1817816468 -0.9882730290 0.9877821493
## [2206] -1.4866855875 0.5054961379 -0.0408883574 -0.2830319401 1.4165322948
## [2211] -0.8320986568 -0.9475680024 -0.9693524859 1.0980219349 0.9167347655
## [2216] -0.7719407677 0.5207520934 -1.0395532585 -0.0356939806 0.4730480749
## [2221] -0.8832281692 2.3620218625 -0.8538012828 -0.7240758457 -1.1096405255
## [2226] 1.7456650068 0.2727460075 -1.0492111169 0.0225118716 -1.0612730565
## [2231] -0.3801267360 0.8018674040 -0.0556200221 0.8648017390 -1.0981939938
## [2236] -0.6641616975 -0.9984792521 2.2677082366 1.6358160519 -0.8417532474
## [2241] 0.8035062586 -0.6150133677 0.6119721378 0.9035515103 -0.6371311137
## [2246] 1.1349627520 -0.7717896969 -1.0056439424 -0.9981153371 0.4908271764
## [2251] 0.0071342325 -0.8524579499 -0.1261328172 -0.7530902958 -0.2004339971
## [2256] -0.0430427940 -0.6876664451 0.4521771745 -0.6527421559 -1.0362821229
## [2261] -1.0250406206 0.5015928789 0.1640916774 -0.8459800418 -0.6125247207
## [2266] -0.1369083470 -0.2676393264 0.7919904073 -0.3070323815 0.2611769553
## [2271] -0.8448925231 -0.9453041428 -1.0208340625 0.4924499604 0.0456031577
## [2276] -0.8051747851 -0.3117503226 -0.4766586558 -0.4615322387 0.3548717592
## [2281] -0.7332645213 0.7618079020 -1.1194643130 -0.9965840555 -1.2758021211
## [2286] 0.2436634191 -0.3094387321 -1.1734269787 -0.5461045563 -0.7502905813
## [2291] 0.0226741208 0.2067274815 -0.8498653224 1.4947174966 -0.4945690686
## [2296] -1.0916476827 -1.0743779290 2.2566150588 1.3442604277 -1.2809589469
## [2301] 0.1342439996 -0.6429054786 0.4732658475 1.7659255111 -1.4552347990
## [2306] 2.2684699764 -0.8696521819 -1.3152739950 -1.0106918835 1.1726608589
## [2311] 0.5227541043 -1.4395279702 0.2190068792 -0.4323506406 0.4050195647
## [2316] 1.9513051833 -0.1239179407 1.2437319006 -1.1639506241 -1.1164216004
## [2321] -1.1733857947 1.4190521269 1.1559733526 -0.9746984795 -0.1469672431
## [2326] -0.4514422828 0.4429184129 1.3759710966 -0.3615325289 1.9634268595
## [2331] -0.7860777460 -1.1389428130 -0.9111542289 2.3138254488 1.4091641527
## [2336] -1.0662396205 0.5743973780 -0.2462160928 0.9286656753 0.8111495877
## [2341] -0.5288852322 1.6025718242 -0.9030569280 -1.1516684436 -1.0544321048
## [2346] 2.2706268218 1.0147410264 -1.2587979447 0.9565188650 -0.8903028301
## [2351] -0.0366173738 2.0271323944 -0.4289644423 1.9420265075 -0.8344565051
## [2356] -1.0470345180 -1.1289629041 2.3630017743 1.1507936845 -0.9141130079
## [2361] 0.1394000166 -0.3214609961 0.3916810151 1.3048657212 -0.1918149851
## [2366] 2.1098955283 -0.7368745714 -1.2608065118 -1.2201283008 1.6757774794
## [2371] 1.1835769548 -1.3286200825 0.3953683799 -0.1479903898 0.3484288833
## [2376] 1.2855171699 -0.2765565643 2.6405889083 -0.6216923529 -1.2729708096
## [2381] -1.1543425939 1.2092868237 1.1745906538 -1.1537725567 0.4743199551
## [2386] -0.2986834104 0.7353385130 1.2791572572 -0.1471599309 1.1238612671
## [2391] -0.3911402033 -0.4503250386 -0.2458005139 0.2149161992 0.2768090915
## [2396] -0.4063194160 -0.0447220032 -0.4234627590 -0.4084294018 -0.3049295784
## [2401] -0.2598226148 0.4706876644 -0.4677164567 -0.3756495692 -0.3789260176
## [2406] 0.6770820436 0.0450127244 -0.4495492679 -0.4673176528 -0.3641781048
## [2411] -0.2942668427 -0.1793145920 -0.5003518947 0.5872230879 -0.4555794966
## [2416] -0.4947338693 -0.3866654243 0.8251698665 0.0478838266 -0.4385091415
## [2421] -0.2461503088 -0.5671011864 -0.5479617419 0.0310047193 -0.5952602261
## [2426] 0.2692685045 -0.4960367558 -0.5243710439 -0.4998867537 0.0797879552
## [2431] -0.0530442867 -0.3759040761 -0.4118558638 -0.6065783512 -0.3482089706
## [2436] 0.5079331245 1.6817505266 -0.7249779434 -0.4020522483 -0.3512731081
## [2441] -0.6277756708 -0.7934166174 3.8598945173 0.1744710596 1.6297345770
## [2446] -1.0439731453 0.5206908008 4.7088384113 -0.6727064017 -0.7047948190
## [2451] 1.2168880590 -0.8974139899 -0.5190509299 -1.3391058506 2.4241764511
## [2456] -0.2481003916 -0.6235107999 -0.5282214678 -1.1363358331 -0.4510505902
## [2461] -0.0604946750 -0.2587880690 1.2060664949 -0.5124311385 -0.8352308368
## [2466] -0.8572269009 0.3951561331 -0.3669818830 -1.3565346681 -0.6995754135
## [2471] -0.7702097724 -0.5145616858 0.5488083484 -0.8904854780 1.0748584155
## [2476] -1.4242275947 -0.4494451441 -1.0412277532 0.9066002982 -0.7854682432
## [2481] -0.8476973085 0.1501279229 -1.1452375913 -0.4801128861 1.6127270376
## [2486] -0.3706659588 0.2590068333 -1.0014356857 -1.4591980438 -0.8522675638
## [2491] 2.5552660322 -0.3018253772 -0.7025008616 -0.3970178482 -0.9320400684
## [2496] 0.2634667570 0.2783666506 -0.2598034309 1.7359505524 -0.4101163508
## [2501] -0.1908906383 -0.1401943803 1.6588930116 0.9117260054 -0.6415733767
## [2506] 0.2101252677 0.2961065166 -0.8949875207 1.2361023319 0.1155359626
## [2511] 1.7855715313 -0.9106378405 -0.5257732207 -0.5736621846 1.2021336167
## [2516] 2.0211823034 -1.0885599547 0.4666000307 0.0963800679 -0.1130504352
## [2521] 0.3866858030 -0.1029057114 1.4507297797 -0.4035064599 -1.2247210205
## [2526] -0.4103760921 0.8663461125 0.4998841765 -0.6520184120 0.6902666320
## [2531] -1.6984388022 -1.2288051462 0.4370795409 -0.7869296615 1.7223507764
## [2536] 0.0007466072 -0.4254443165 -0.4092021103 1.7913273220 0.8464150119
## [2541] -1.5081349640 0.1258136062 -1.3356580452 0.9683650397 0.7948513848
## [2546] -0.5610057022 1.0266141941 -0.8042854886 -0.5397149233 -1.3933484179
## [2551] 2.0253378883 -0.2506973278 -0.2356841753 1.2680971279 -0.5336038576
## [2556] 0.7784331298 0.6517747504 -0.3211687762 0.6684401285 -1.4751436392
## [2561] 0.2675142058 -0.6394141220 0.4533918477 0.8395606119 1.2290421403
## [2566] 1.1012212478 0.3129479308 0.3679721431 0.0539152264 0.3847325750
## [2571] 1.4439644623 -0.9093117909 -0.1402622513 -1.3849498332 0.9706336582
## [2576] 0.0032204605 0.4783064501 0.2709440644 -0.7233850227 -0.3027398527
## [2581] 0.4892776611 0.7967510415 1.3168352138 -0.6918341112 -0.7321050633
## [2586] -0.9351064367 1.5116180567 1.0935240664 -0.3080577524 0.0725239135
## [2591] -1.3990291078 -0.6834205123 0.0618760056 -0.0500140364 1.0029430676
## [2596] 0.1273747581 0.0786156504 0.0950396260 1.1232311239 0.1458824764
## [2601] -0.0184959899 -0.1057983496 -0.1168083438 0.7014305943 0.7353326269
## [2606] -0.2034255805 1.6483576590 -0.0981636497 -0.0574501234 -0.0727016286
## [2611] 0.5628425595 -0.0188844736 -0.1980364290 -0.2341382682 -0.2469009936
## [2616] 0.0537054632 1.7575840799 -0.2796973619 2.0991113916 -0.1591416834
## [2621] -0.0709539477 -0.1652316056 0.8961530201 -0.2574622685 -0.2829940814
## [2626] -0.0769143583 -0.2365704644 0.3943690930 2.0867859843 -0.3984118621
## [2631] 0.7725223705 -0.1888832588 -0.3207176740 -0.2463966032 1.1907754600
## [2636] -0.0807303477 -0.3151961258 -0.2369747834 -0.3610582426 0.4489165334
## [2641] 0.9142767931 -0.5694278210 1.4990373360 -0.6910857227 -0.4839572795
## [2646] -0.6575019423 1.9036971369 0.0707413250 -0.7061782588 -0.4231754904
## [2651] -0.4394635820 -0.3684363518 1.3015674929 -0.5149638345 1.6306693717
## [2656] -1.0840231602 -0.6491568977 -0.9988338133 1.1053093150 0.6811860574
## [2661] -0.7242704353 0.2721144685 -0.8407439629 0.3264752767 0.2672237308
## [2666] -0.4858078967 1.1865850934 -1.0142047491 -0.9112973019 -1.0052590503
## [2671] 0.3101899394 0.2708132312 -0.8412471679 -0.1358247562 -1.0404184706
## [2676] -0.5880382802 0.5769158694 -0.8795245289 1.9172844726 -0.7798870065
## [2681] -0.7420982072 -0.6833267390 1.8902768450 -0.0633555113 -1.0093525832
## [2686] -0.2564927135 -1.0260657425 -0.2360415261 0.9671368189 -0.6971019649
## [2691] 1.5763173893 -0.8697724520 -0.8386101856 -0.9134923878 1.7183005232
## [2696] 0.0898226649 -0.7712439992 0.2416827170 -1.0286228440 0.1352445185
## [2701] 0.0133704591 -0.5521312616 1.1677306215 -0.9938051816 -0.5554431666
## [2706] -0.8204810840 0.5444116688 0.2101345006 -0.3856052380 -0.2874943486
## [2711] -0.5467424306 -0.4623430948 0.1020790334 -0.5925726182 1.6472141620
## [2716] -0.7985241696 -0.8227081466 -1.0018867557 0.5170167894 -0.4406953290
## [2721] -0.7166822523 -0.5191678677 -0.7936776032 -0.4322567637 1.3999110438
## [2726] -0.4830924542 0.5824633685 -0.9064376427 -0.7618701018 -0.8452863264
## [2731] 2.6044260661 0.6262535208 -0.6669540548 -0.4261486592 -0.9832914125
## [2736] -0.3937357754 0.2962796789 -0.0505083274 0.9928480885 -1.4099998758
## [2741] -1.3459169206 -1.4347542996 1.6380033532 0.4704780193 -0.8652451590
## [2746] 0.7283589250 -0.4437030603 0.0015273676 0.0978663517 -0.7677662977
## [2751] 1.0620791495 -1.0521920684 -1.4242558411 -1.4049134402 1.9617838252
## [2756] 1.5184710445 -0.9312976565 0.0903781554 -0.7938306902 -0.4436609005
## [2761] 0.4272633849 -0.3938623817 1.3351036245 -1.3406712948 -1.1808082561
## [2766] -1.3346204183 1.6151826829 1.3623648549 -0.6153388461 1.1053430898
## [2771] -0.4827417971 -0.7208766943 0.5098760853 -0.6683665484 0.9248444969
## [2776] -1.6150189033 -1.5346742324 -1.5155611388 1.3357879323 0.5545860095
## [2781] -1.4446459613 0.4671256117 -1.2450173379 -0.1044163228 0.9284682785
## [2786] -0.8854165797 1.6537430509 -1.0781342495 -1.5038065123 -1.5230631305
## [2791] 1.6125561831 1.2064578232 -1.5411032151 0.6277850368 -1.2510902604
## [2796] -0.2373862288 1.6937475117 -0.3664184936 1.5799097158 -1.3286700387
## [2801] -1.6209325827 -1.5101398482 2.4978917086 1.1008179366 -1.8083715571
## [2806] 1.5555541298 -0.1836604699 0.0471330619 1.5816206882 0.2259480095
## [2811] 2.0191476001 -1.4484945332 -1.5662401243 -1.5390506276 1.9225915011
## [2816] 2.0354143214 -0.9313582139 1.1087474935 -0.4144533551 0.0614352322
## [2821] 1.8249172781 -0.5216753302 1.4835640603 -1.4266953761 -1.3780229571
## [2826] -1.3375762911 0.8735574035 0.7541063157 -1.2100529637 -0.1950427667
## [2831] -0.6301344633 0.2541875186 2.0909416741 -1.0587722031 1.4500290893
## [2836] -1.0720644435 -1.5294518526 -1.6757765994 3.0404363268 1.6901669267
## [2841] -1.2854154737 0.8171660936 -1.2884325310 -0.2744886197 1.3410837742
## [2846] -0.5523499348 2.1455030783 -1.4094244257 -1.5684167406 -1.2945553694
## [2851] 2.2475901804 1.1608908728 -1.2885362547 -0.5216739422 -0.9766555691
## [2856] 0.5222612116 1.5732950524 -0.7392843878 2.2176763158 -1.3427895169
## [2861] -1.5361500222 -1.5376766497 2.2296549506 2.5233939673 -0.9939152723
## [2866] 0.4064191765 -0.4489353774 -0.2555016498 0.8738562673 -0.1368584283
## [2871] 1.5776699777 -0.9901919882 -1.5605405811 -1.5095063249 0.6851535183
## [2876] 2.1040381391 -0.9241536662 1.2665438926 -0.2814039827 0.0021500424
## [2881] 0.6175146061 -0.3896903144 1.0422668108 -0.5516897437 -0.5132595430
## [2886] -0.4960638297 1.6816473117 1.4287112214 -0.5611323453 0.0618749024
## [2891] -0.6442479884 0.0080579925 0.5298386521 -0.5978937544 1.1998657425
## [2896] -0.5553827298 -0.4988378878 -0.5013045826 1.5480384538 1.0798932891
## [2901] -0.4911345897 -0.4232655972 -0.4767614784 -0.1257728361 1.2166041753
## [2906] -0.6621014670 1.6728550942 -0.6075267089 -0.5772248634 -0.5687751964
## [2911] 1.3133811850 0.6889444714 -0.6208061072 -0.1297133604 -0.6687380086
## [2916] -0.1270908198 0.5458580650 -0.7001189092 0.7841486488 -0.7490492198
## [2921] -0.6563089677 -0.6921289760 1.3678897452 1.6426245307 -0.6571443675
## [2926] -0.1607754656 -0.8128296686 -0.5743361033 0.5480612612 -0.8105283805
## [2931] 1.8499562513 -0.8004303293 -0.7194792385 -0.7825019617 2.2885983666
## [2936] 1.6308950285 -0.7848128544 -0.3591091597 -0.7153079934 -0.2168227237
## [2941] 0.7439855945 -0.9207503893 1.0549257061 -0.9713516403 -0.8601592687
## [2946] -0.8806595467 1.5756920036 0.5928546404 -0.9814147525 -0.1556976314
## [2951] -0.7429658570 0.1556227552 0.5865813248 -1.1126080227 1.4174841683
## [2956] -0.9658926206 -0.9084158421 -0.9822603534 1.6650629263 1.4130487029
## [2961] -1.0597609339 -0.2602446674 -0.7047641226 -0.4780315073 0.4988023338
## [2966] -1.0747788862 2.5095856561 -1.0481423283 -0.9019413109 -0.9419634189
## [2971] 2.4181369366 1.1412476654 -0.9895658256 -1.0741389977 -0.8830856110
## [2976] -0.1602433755 0.9809638705 -0.9070959882 1.5228352978 -1.0326773744
## [2981] -0.8405395423 -0.9494059721 1.7283809751 1.4985636737 -0.9476447413
## [2986] 0.0119119680 -0.8823735180 0.0487356670 0.9902869313 -0.8795196785
## [2991] 0.8257144152 -0.9729289515 -0.7623677930 -0.8589288981 2.1827667435
## [2996] 1.1400287677 -0.9208035192 -0.2887231373 -0.8892834996 0.3670163568
## [3001] 0.9439358519 -0.9124603391 1.7939325190 -0.9876129480 -0.8088360113
## [3006] -0.9367056045 1.8154319501 0.6387138009 -0.8997764379 -0.6426043680
## [3011] -0.8528147960 -0.0692141458 0.4436893124 -0.9657832147 1.5201977759
## [3016] -0.9564035872 -0.8988612354 -1.0330844334 2.0742358650 0.9296161774
## [3021] -1.0066133295 -0.8963655650 -0.6345555237 0.6550849534 0.8883743070
## [3026] -0.2564801049 1.7689246048 -0.1146519166 -0.4262024480 -0.3591364839
## [3031] 1.7695984757 1.0102498315 -0.3117625995 -0.2630400310 -0.1034555592
## [3036] 1.0867486758 0.7154005508 -0.8146153418 2.5409697918 -0.1727806207
## [3041] -0.5772078825 -0.4201658866 2.8101999362 0.7383916521 -0.6878377373
## [3046] -0.4033348008 -0.2066454834 0.1918997996 1.8765384404 -0.3360042404
## [3051] 2.3560382925 -0.3028980383 -0.4535779900 -0.2717533886 2.5091616280
## [3056] 0.6492862804 -0.6373326033 0.2767380307 -0.3141948152 -0.3046103610
## [3061] 1.9075155174 -0.7240788165 1.5788128281 -0.5629445843 -0.5279386094
## [3066] -0.5042558035 2.4702004857 1.2132577907 -0.6378537247 0.0552337314
## [3071] -0.5978479303 0.3798553548 0.9002686621 -0.9483380410 1.2683700995
## [3076] -1.0624923266 -1.0375387963 -0.9443827390 2.1933607155 0.2439340256
## [3081] -1.1554146696 -0.3741698424 -1.0400430491 0.2223307703 0.9709726803
## [3086] -0.3845944714 1.8343091512 -1.1213048105 -1.0089319189 -1.0038319658
## [3091] 1.7781168715 1.2705005118 -1.0224719935 -0.3795456389 -1.0068766745
## [3096] 0.3410926540 0.4662434907 -0.6596152190 1.0543655477 -1.2215258719
## [3101] -0.7133986614 -1.1120626025 0.9346309318 1.4210115890 -0.7715676086
## [3106] -0.3492194818 -0.5889666195 -0.6642936865 0.5645465013 -1.0323179980
## [3111] 1.7023815711 -0.9045655024 -1.2289522665 -1.0651881083 3.1414132665
## [3116] 1.1150410018 -1.1923498384 -0.3282653671 -1.2832184550 -0.6852074879
## [3121] 0.0843342745 -1.2807985009 1.3125745033 -0.9311208737 -1.3061294044
## [3126] -1.2305434059 1.7872044002 0.4955235194 -1.3171903308 -0.1823720260
## [3131] -0.9843918554 -0.6363296029 0.0170539880 -0.9399693552 1.3431160826
## [3136] -1.2147212243 -1.2595029299 -0.9271867652 1.4460892382 0.7070562177
## [3141] -1.2154646245 -0.8535749067 -1.1763710084 -1.1418008897 0.2122497312
## [3146] -1.2352841886 2.2248589882 -1.0213525280 -1.0794840785 -1.2476286747
## [3151] 2.1244406706 0.1122165929 -1.3166602254 -0.6232440305 -1.1036786026
## [3156] -0.5117516403 0.7968126324 -1.0234044693 0.6206735645 -1.3060382816
## [3161] -1.2409300221 -0.9756482000 2.6171200251 1.1514707709 -0.9309951420
## [3166] -0.7675503882 -0.7578801152 -0.1077703624 1.1056516773 -0.0728371014
## [3171] 0.5163086497 -1.1824252599 -0.9903981545 -1.1137319562 1.1939613409
## [3176] 1.3469294712 -0.7241145484 0.2391829972 -0.4666708183 -0.1427146681
## [3181] 0.1579047909 -0.6023889983 1.3017938344 -1.1533985480 -0.9653116984
## [3186] -1.1868008317 0.8749550509 1.0242860099 -0.9256457578 1.1139615022
## [3191] -0.9470056246 -0.0823618614 1.1483153777 -0.5130691307 1.2707474491
## [3196] -1.2853419424 -0.8883075147 -1.1204977065 1.4829795055 0.8694317053
## [3201] -0.9634193165 0.2759629535 -1.3217745073 -1.0185010571 1.1698395749
## [3206] -1.1492725956 1.4514540966 -1.3428039943 -1.2707882871 -1.3884373113
## [3211] 0.9774109957 0.6463806096 -1.1272722659 0.4092201392 -1.2169533265
## [3216] -0.4390120555 1.1220529820 -0.7936590060 2.7262658584 -1.2742897911
## [3221] -0.8464786407 -1.0566858702 3.2786667757 2.0389154880 -0.8824777308
## [3226] 0.6096203958 -0.6347068287 -0.2454105146 0.7030584808 0.2238876829
## [3231] 1.7089358876 -1.6379697840 -1.0264975014 -1.2157605847 0.9363362457
## [3236] 1.7720782668 -0.9989301481 1.7498938984 -1.0489461587 -0.2725981733
## [3241] 1.0891594589 -0.9675035107 2.1098384141 -1.4307558500 -1.2907192108
## [3246] -1.5308242847 1.8652398642 1.8523345283 -1.3180336320 0.5541340426
## [3251] -0.4916078023 -1.1157604972 0.7505127436 -0.0359715432 2.6470892386
## [3256] -1.5528983659 -1.0764498593 -1.1724295918 2.1524997307 1.6976940881
## [3261] -1.0890002359 0.9273890547 -1.2669808357 -0.4902698923 1.3310242960
## [3266] -0.9837643578 2.0421707057 -1.4313130978 -1.0219937573 -1.4275471949
## [3271] 1.9651738147 1.0065214630 -1.0948096161 1.2141179320 -1.2263659093
## [3276] 0.2753757941 1.1368315039 0.2563717727 0.8314323654 -1.4383747264
## [3281] -0.8307724511 -1.2530499012 2.0267284497 1.1354353525 -0.7461224629
## [3286] 1.2136215325 -0.9483845947 -0.2815676579 0.7715508438 -1.1421454104
## [3291] 0.9764870073 -1.3147185050 -1.0205574743 -1.3826382392 1.4560530088
## [3296] 1.4285737465 -1.0663967887 0.5704634477 -1.2201732696 -0.7985798235
## [3301] 1.1253714872 -1.1193790539 1.5532580749 -1.5062951289 -1.0190929471
## [3306] -1.2730671005 2.0493258127 2.2482961063 -1.1757286057 0.2054641702
## [3311] -0.9623486786 0.6647932882 0.5413253144 0.1018223134 0.6635004952
## [3316] 0.2032847418 0.2371824865 0.2315842250 0.7142000600 0.2579239910
## [3321] 0.1843153967 0.0787340592 0.1244695003 0.6710602548 0.5859018449
## [3326] 0.0806898733 1.0699329688 0.2275256364 0.1639188987 0.1715671422
## [3331] 0.5267633796 0.1334519280 0.0928001516 -0.0175634361 0.0613368066
## [3336] 0.2715317902 1.1975333061 -0.0435406846 1.2580115699 0.0708569423
## [3341] 0.2252076179 0.1084290185 0.6474196157 0.0542490178 0.0075403110
## [3346] 0.0161288595 0.0029528584 0.3451374869 1.3050684797 -0.1045658565
## [3351] 0.6178285820 -0.0122095380 0.0013174257 -0.0195647566 0.8211072660
## [3356] 0.0865020938 -0.0746959108 -0.0693267619 -0.1248803751 0.4450733009
## [3361] 0.6843654904 -0.3836670210 0.7077711849 -0.3853170669 -0.1696159195
## [3366] -0.3053790917 1.0368504793 -0.1221888362 -0.3722713784 -0.3973467711
## [3371] -0.3061096290 0.0145777955 0.6470918686 -0.4518964058 0.6693640964
## [3376] -0.6261326804 -0.4356780404 -0.5483485941 0.4243061024 0.2214168591
## [3381] -0.4970437847 -0.2062574758 -0.5586817598 0.2265935200 0.0985902445
## [3386] -0.4888926752 0.5123592735 -0.6425981205 -0.5096830263 -0.5993025107
## [3391] -0.0553545974 0.0089243438 -0.5878641403 -0.2088417297 -0.6633388233
## [3396] -0.4864864776 0.1399483680 -0.5940568795 1.0973751180 -0.4939213385
## [3401] -0.4669259991 -0.4856674997 0.8985477926 -0.1207875300 -0.6150221652
## [3406] -0.4425198073 -0.6634291183 -0.1825312780 0.3723004491 -0.5011875245
## [3411] 0.8961651930 -0.5013738652 -0.4734371566 -0.5559194642 0.7748815143
## [3416] 0.0343373914 -0.5165152467 -0.1923746187 -0.5897725544 -0.0988156295
## [3421] -0.1361259683 -0.3820249720 0.5764304395 -0.5731070888 -0.3126685684
## [3426] -0.4441362607 0.1524189397 -0.1223589762 -0.3380421121 -0.3927793002
## [3431] -0.4830413737 -0.3261840598 0.0475177806 -0.4164266046 0.8561922609
## [3436] -0.4184923221 -0.4360540802 -0.5665368726 0.3884524898 -0.3210699885
## [3441] -0.4570139049 -0.5322346085 -0.4424329870 -0.2224603646 0.7775398126
## [3446] -0.3956778337 0.6375015865 -0.5748331564 -0.4526314114 -0.4879474664
## [3451] 1.1987346389 0.2307197556 -0.4411512635 -0.4851879888 -0.5720247854
## [3456] -0.0939870269 0.2353909098# add the residuals as a new column into the HWI_grouped_species dataframe ----
mean_ndvi_df$residuals <- residuals(ndvi2010_2021_gam)
# looking at the distribution of the residuals
hist(mean_ndvi_df$residuals)
Since there wasn’t enough data for modelling, we downloaded 10 more years of daily ADVRR NDVI data of 5km resolution for 2000-2009 and repeated the same procedures to enlarge the dataset for our NDVI GAM.
# extracting all links for 2000-2009 ----
# loop for 2000
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2000/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2000ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2001
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2001/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2001ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2002
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2002/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2002ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> then probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2003
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2003/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2003ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2004
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2004/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2004ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2005
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2005/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2005ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2006
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2006/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2006ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2007
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2007/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2007ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2008
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2008/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2008ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}
# loop for 2009
url <- "https://www.ncei.noaa.gov/data/land-normalized-difference-vegetation-index/access/2009/"
pg <- read_html(url)
linkys <- html_attr(html_nodes(pg, "a"), "href")
LINKS <- list()
for(i in 1:length(linkys)){
link <- paste(url, linkys[i], sep = "")
LINKS[i] <- link
}
LINKS <- do.call(rbind, LINKS)
for(j in 6:length(linkys)){
url_path <- paste(url, linkys[j], sep = "")
path <- paste("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/ndvi/2009ndvi/",linkys[j], sep="")
try(download.file(url_path, destfile = path, mode = "wb")) #add mode = wb and now it works --> the probably won't have to run corrupt file unless things don't work
Sys.sleep(5)
}# cropping the ndvi to parks and taking mean monthly ndvi for 2000-2009 ----
nc.year_dir <- "data/ndvi/ndvi00-09"
# setwd(nc.year_dir)
# import all of the boundaries for Canadian parks
CAshape <- st_read("data/shapefiles/ca_provinces/CLAB_CA_2023-09-08")
# Create a list of the names of the 25 parks to be studied
test_parks <- c("WATE", "ELKI", "JASP", "WOOD",
"BANF", "YOHO", "KOOT", "REVE",
"PRIM", "GLAC", "WAPU", "FUND",
"KOUC", "NOVA", "KEJI", "AULA",
"NAHA", "FIVE", "PELE", "GBIS",
"THIS", "PEIS", "FORI", "PALB", "IVVA")
# import JASP shapefile
jasper_shape <- readRDS("data/shapefiles/parks_polygons/jasper.rds")
# Define the CRS
CRS_canada <- crs(jasper_shape)
# List all year folders in the ndvi directory
year_folders <- list.dirs(path = nc.year_dir, full.names = TRUE, recursive = FALSE)
RESULTS_2 <- list()
# Loop through each year folder
for (i in 1:length(year_folders)) {
year <- gsub(pattern = "ndvi",
replacement = "",
x = gsub(pattern = "data/ndvi/ndvi00-09/",
replacement = "",
x = year_folders[i]))
# List all month folders in the year folder
month_folders <- list.dirs(path = year_folders[i],
full.names = TRUE,
recursive = FALSE)
# Generate an empty list for storing daily results
res_month <- list()
# Loop through each month folder
for (j in 1:length(month_folders)) {
# Make a list of the files in the month directory
nc.files <- list.files(path = month_folders[j],
pattern = "*.nc",
full.names = TRUE)
# Generate an empty list for storing daily results
res_day <- list()
# Loop through all the ndvi files for the current month
for (k in 1:length(nc.files)) {
# make the spatrasters
spat <- rast(nc.files[k])
spat <- spat[[which(names(spat) == "NDVI")]]
# Reproject the raster to the CRS of jasper_shape
reprojected_spat <- terra::project(spat,
CRS_canada,
method = "near")
# Generate an empty list for storing results
res <- list()
#Loop over the vector of park names to extract the NDVI information
for(l in 1:length(test_parks)){
#Extract the desired park contour
PARK <- CAshape[CAshape$CLAB_ID %in% test_parks[l],]
# crop the NDVI raster to the park
cropped_spat <- crop(reprojected_spat, PARK, mask = TRUE)
# Get mean and variance in NDVI
NDVI <- mean(values(cropped_spat), na.rm = TRUE)
#NDVI_var <- var(cropped_spat)
NDVI_var <- var(values(cropped_spat), na.rm = TRUE)
# Store as a data frame in the list
res[[l]] <- data.frame(park = test_parks[l],
date = paste(year,j,k,sep = "_"),
ndvi = NDVI,
ndvi_var = NDVI_var)
} #close the loop over parks
#clean up the results over the days of the month
res_day[[k]] <- do.call(rbind,res)
} #close of day loop
#clean up the results over the months of the year
res_month[[j]] <- do.call(rbind,res_day)
} # close of the month loop
#clean up the results over the months of the year
RESULTS_2[[i]] <- do.call(rbind,res_month)
} # close of year loop
#SAVE AS RDA OR CSV
save(RESULTS_2, file = "test.rda")
# convert the final list to a data frame (daily ndvi mean and var)
RESULTS_2 <- do.call(rbind,RESULTS_2)
write.csv(RESULTS_2, "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/morendvi.csv", row.names=FALSE)
RESULTS2_df <- read.csv("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/morendvi.csv")
# close loop of all the years #Create data frame by grouping park means according to months and years ----
#convert to calendar dates
RESULTS2_df$date <- as.Date(RESULTS2_df$date, format = "%Y_%m_%d")
#extract year
RESULTS2_df$year <- lubridate::year(RESULTS2_df$date)
#extract month
RESULTS2_df$month <- lubridate::month(RESULTS2_df$date)
#rename columns
names(RESULTS2_df)[3] <- "ndvi_daily_mean"
names(RESULTS2_df)[4] <- "ndvi_daily_variance"
# Create a new dataframe for analysis for monthly ndvi mean to be grouped by park and year
more_data_ndvi_mean <- aggregate(ndvi_daily_mean ~ month + year + park, data = RESULTS2_df, FUN = mean, na.rm = TRUE)
#rename columns
names(more_data_ndvi_mean)[4] <- "ndvi_monthly_mean"
#save datafram as a csv
write.csv(more_data_ndvi_mean, "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/more_monthly_mean_ndvi.csv", row.names=FALSE)
more_mean_ndvi_df <- read.csv("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/more_monthly_mean_ndvi.csv")
# preparing for GAM ----
# rescale ndvi in dataframe
more_mean_ndvi_df <- more_mean_ndvi_df %>%
mutate((ndvi_monthly_mean+1)/2)
# rename columns
names(more_mean_ndvi_df)[5] <- "scaled_mean_ndvi"
# change month and year to numeric
as.numeric(more_mean_ndvi_df$month)
as.numeric(more_mean_ndvi_df$year)
# merge to form data frame with 2000-2021 data frame ----
NDVI_2000_2021 <- rbind(more_mean_ndvi_df,mean_ndvi_df)
#save datafram as a csv
write.csv(NDVI_2000_2021, "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/NDVI_2000_2021.csv", row.names=FALSE)
NDVI_2000_2021 <- read.csv("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/NDVI_2000_2021.csv")#Convert PARK ID to a factor
NDVI_2000_2021$park <- as.factor(NDVI_2000_2021$park)# NDVI & parks GAM! ----
# BAM in parks, month, year
# predicts NDVI from 2000-2021 (based on these variables how do they affect NDVI)
# looks at NDVI changes
all_ndvi_gam <-
bam(
scaled_mean_ndvi ~ #scale ndvi from 0 to 1 to fit beta distribution
# fixed effects
park +
# global smooths
s(month, park, bs = "fs", k = 8, xt = list(bs = "cc")) + #based on month and park
s(year, park, bs = "fs", k = 8) + #based on year and park
ti(month, year, k = 6), #based on month and year
family = "betar",
#beta location scale distribution for the data
data = NDVI_2000_2021,
method = 'fREML'
)
saveRDS(all_ndvi_gam, file= "data/models/all_ndvi_gam")
all_ndvi_gam <- readRDS("data/models/all_ndvi_gam")summary(all_ndvi_gam)##
## Family: Beta regression(137.422)
## Link function: logit
##
## Formula:
## scaled_mean_ndvi ~ park + s(month, park, bs = "fs", k = 8, xt = list(bs = "cc")) +
## s(year, park, bs = "fs", k = 8) + ti(month, year, k = 6)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.04907 0.04026 1.219 0.222907
## parkBANF 0.11363 0.05636 2.016 0.043812 *
## parkELKI 0.34967 0.05641 6.199 6.05e-10 ***
## parkFIVE 0.37341 0.05641 6.620 3.90e-11 ***
## parkFORI 0.31043 0.05639 5.505 3.84e-08 ***
## parkFUND 0.41875 0.05641 7.423 1.30e-13 ***
## parkGBIS 0.36301 0.05640 6.436 1.32e-10 ***
## parkGLAC 0.10390 0.05636 1.844 0.065286 .
## parkIVVA 0.16138 0.05671 2.846 0.004447 **
## parkJASP 0.11218 0.05636 1.990 0.046582 *
## parkKEJI 0.43458 0.05642 7.703 1.54e-14 ***
## parkKOOT 0.15719 0.05636 2.789 0.005303 **
## parkKOUC 0.26701 0.05638 4.736 2.23e-06 ***
## parkNAHA 0.13614 0.05636 2.415 0.015743 *
## parkNOVA 0.22312 0.05637 3.958 7.64e-05 ***
## parkPALB 0.31044 0.05639 5.505 3.84e-08 ***
## parkPEIS 0.20556 0.05637 3.646 0.000268 ***
## parkPELE 0.10100 0.05922 1.706 0.088151 .
## parkPRIM 0.45491 0.05642 8.063 8.85e-16 ***
## parkREVE 0.19774 0.05637 3.508 0.000455 ***
## parkTHIS 0.36057 0.05640 6.393 1.75e-10 ***
## parkWAPU 0.07194 0.05636 1.276 0.201859
## parkWATE 0.32641 0.05639 5.788 7.47e-09 ***
## parkWOOD 0.26542 0.05638 4.707 2.57e-06 ***
## parkYOHO 0.08695 0.05635 1.543 0.122919
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(month,park) 146.341 150.00 39.848 <2e-16 ***
## s(year,park) 94.696 175.00 7.290 <2e-16 ***
## ti(month,year) 9.162 11.64 6.439 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.621 Deviance explained = 64.3%
## fREML = 9826.6 Scale est. = 1 n = 6407bam_plot <- plot(all_ndvi_gam, pages = 1, scheme = 2)
# residuals of model 1
residuals(all_ndvi_gam)## [1] -4.900959e-02 3.302876e-02 1.581615e+00 1.687079e-02 6.662772e-02
## [6] 1.190487e-01 1.549103e-02 6.930489e-01 4.221600e-01 -3.602674e-01
## [11] -6.053333e-01 1.072459e+00 -1.371003e-01 -2.592988e-01 2.577482e-02
## [16] -3.365299e-01 4.947581e-01 -5.046150e-03 1.527910e+00 -1.508618e+00
## [21] -8.085124e-01 -4.534565e-01 -7.832670e-02 1.267826e-01 -1.821243e-01
## [26] -1.969142e-02 7.228307e-02 -2.178465e-01 -3.603697e-01 -3.567183e-01
## [31] -6.187569e-01 -6.884489e-01 2.285740e-01 -1.043716e-01 4.698669e-02
## [36] -3.666932e-02 -1.360536e-01 -8.423229e-01 -2.041980e-01 -4.027415e-01
## [41] -4.259024e-01 3.313987e-01 1.377142e-01 8.551150e-02 -1.457547e-01
## [46] -1.180455e-01 -5.777504e-01 2.381830e-02 -6.965988e-01 3.797347e-01
## [51] 3.861670e-01 6.596497e-02 2.302482e-01 4.700507e-01 -1.977952e-01
## [56] 7.278223e-01 -1.489372e-01 -2.276213e-01 -1.334307e-01 3.629010e-01
## [61] -1.192932e-01 9.964730e-02 6.555079e-01 -2.791540e-01 1.782788e-01
## [66] -8.269376e-03 6.332659e-01 -1.768306e-01 3.219980e-01 -4.406938e-02
## [71] 8.378243e-02 3.004017e-01 -2.550564e-01 -3.723998e-01 -9.844076e-02
## [76] 5.015672e-01 4.455508e-01 2.622128e-01 -1.277462e-02 1.152996e-01
## [81] -1.699131e-01 -2.810869e-01 2.446951e-02 -1.507238e-01 -1.049458e+00
## [86] -5.899957e-01 2.875129e-01 -4.628804e-02 5.843666e-02 1.240029e-01
## [91] -5.078154e-01 3.078407e-01 -6.542649e-01 2.103120e-01 -2.116180e-01
## [96] 6.063138e-02 -1.589477e-01 1.058295e-01 2.385782e-02 2.781557e-01
## [101] 3.770318e-01 4.500692e-01 -7.184320e-01 5.722017e-01 -3.343027e-01
## [106] 1.728128e-01 -1.566113e-02 1.298521e-01 3.233064e-02 9.154337e-02
## [111] 1.735516e-01 -7.887683e-02 3.488682e-01 1.082022e+00 -4.553168e-01
## [116] -1.242637e+00 4.923432e-01 5.505152e-01 -2.358527e-01 4.166528e-01
## [121] 5.961432e-02 -9.373821e-02 -1.379671e-01 4.608678e-02 -1.741268e-01
## [126] 1.202194e-01 -7.299080e-01 1.663006e-01 -5.376240e-01 1.723455e-01
## [131] -1.458618e-01 7.070929e-01 5.733463e-02 -7.065738e-02 -2.437973e-01
## [136] -3.311620e-01 2.793906e-01 3.450620e-01 -5.224962e-01 -3.151039e-01
## [141] -5.641927e-01 3.360301e-01 -3.827033e-01 -1.868362e-01 -9.694038e-02
## [146] 1.375517e-02 -1.102420e-01 -9.094947e-02 1.480627e-01 -5.218953e-02
## [151] -5.198876e-01 4.230338e-01 -3.293118e-01 3.350484e-01 -1.917105e-01
## [156] -2.074563e-01 -2.857801e-01 9.046388e-02 3.178846e-01 5.829954e-02
## [161] -2.294899e-01 -1.360917e-01 -6.085342e-01 3.060707e-01 -5.044090e-01
## [166] 3.735225e-01 -2.127601e-01 4.459430e-01 4.428755e-01 1.049049e-01
## [171] 2.816193e-01 -3.417515e-01 4.355021e-01 4.494386e-01 -8.462867e-01
## [176] 1.092484e-01 -4.526850e-01 1.990481e-01 -3.340104e-01 7.777262e-01
## [181] 8.129450e-02 1.063851e-01 -5.044825e-02 2.959696e-02 -9.063192e-02
## [186] 4.466385e-01 -6.979945e-01 3.287699e-01 -5.004240e-01 3.385467e-01
## [191] -3.238534e-01 1.558996e-01 -9.909814e-02 2.934695e-01 -6.547979e-02
## [196] 1.078512e-01 4.693424e-01 7.379976e-01 -6.883062e-01 5.553557e-01
## [201] -2.670644e-01 6.123025e-01 -7.942569e-02 1.185328e-01 2.029700e-01
## [206] 1.911194e-01 1.180702e-01 -1.616054e-01 -4.605490e-01 1.406433e+00
## [211] -1.308379e+00 8.116979e-01 -1.982509e+00 1.430344e+00 -1.814447e+00
## [216] 8.120991e-03 7.657919e-01 -1.092390e+00 7.399711e-01 -4.306737e-01
## [221] -1.178781e-01 5.052181e-01 -5.115224e-01 4.423119e+00 -2.344516e+00
## [226] 1.802170e+00 -1.255010e+00 -4.659909e-01 -3.207489e-01 -3.642293e-01
## [231] 9.504618e-01 1.788966e-01 3.903322e-01 1.598732e+00 -2.361636e+00
## [236] -3.214530e+00 2.204590e+00 2.826928e+00 -1.434756e+00 8.415055e-01
## [241] 8.455972e-01 -1.600213e+00 4.656991e-01 -3.307101e-01 -8.725924e-02
## [246] 1.195103e+00 -1.957803e+00 2.408653e+00 -1.971676e+00 1.395941e+00
## [251] -1.265334e+00 1.532957e+00 3.665971e-01 -1.930348e+00 9.494378e-01
## [256] -9.824591e-01 2.879038e-01 1.276547e+00 -1.312811e+00 4.441521e-01
## [261] -1.855159e+00 1.440425e+00 -1.590657e+00 -5.201353e-02 1.348829e+00
## [266] -1.712410e+00 3.304401e-01 -1.655545e-01 -2.689040e-01 9.766880e-02
## [271] -9.254667e-01 9.213796e-01 -1.815487e+00 1.759171e+00 -1.771887e+00
## [276] 1.010969e-01 -4.657506e-02 -1.119704e+00 2.028243e+00 -5.940533e-02
## [281] 7.049615e-01 2.772568e-01 -1.039927e+00 1.804960e+00 -2.062910e+00
## [286] 2.535658e+00 -1.218777e+00 1.107296e+00 1.779077e+00 -1.607754e+00
## [291] 1.221721e+00 -1.364572e+00 3.275056e-01 2.943975e-01 -1.864437e+00
## [296] -3.653782e-01 -1.784255e+00 1.652937e+00 -1.755823e+00 2.598659e+00
## [301] 4.997146e-01 -1.885772e+00 1.684432e+00 1.758556e-01 1.080313e+00
## [306] 1.386497e+00 -2.126131e+00 1.080908e+00 -1.740626e+00 1.620363e+00
## [311] -1.616128e+00 1.003783e+00 9.717387e-01 -1.697649e+00 1.024979e+00
## [316] 1.735617e-01 1.056275e+00 1.075706e+00 -1.909631e+00 4.189396e-01
## [321] -1.690131e+00 1.720403e+00 -1.587171e+00 1.847391e-01 3.420642e-02
## [326] -1.651019e+00 9.908499e-01 4.885627e-01 -3.955520e-01 1.822189e+00
## [331] -2.622970e-01 -1.483017e-01 -1.278856e+00 1.428797e+00 -1.204415e+00
## [336] -1.601147e-01 4.776486e-02 1.885421e-01 1.130493e+00 -4.859221e-01
## [341] -8.148505e-01 -5.906084e-01 -3.039780e-01 1.109127e+00 -4.946326e-01
## [346] 1.056316e+00 -1.297734e+00 4.756580e-01 1.326206e+00 -1.374556e+00
## [351] 9.876885e-01 -4.788833e-02 2.181427e-01 4.783627e-01 -2.186252e+00
## [356] -1.041640e+00 3.769206e+00 1.024436e+00 -1.033928e+00 4.397647e-01
## [361] -6.323572e-02 -1.460376e+00 8.123124e-01 -6.436896e-01 -4.145766e-01
## [366] 1.800023e-01 -1.545822e+00 8.765738e-01 -6.155558e-01 1.347208e+00
## [371] -7.612410e-01 7.851606e-03 2.194648e-01 -1.494796e+00 -8.027689e-02
## [376] -8.255071e-02 3.579919e-01 4.768285e-01 -1.195894e+00 -5.169193e-01
## [381] -1.301648e+00 1.586401e+00 -6.205441e-01 2.262837e-01 6.158525e-01
## [386] -1.523857e+00 -1.659464e-01 4.163975e-01 9.941833e-01 2.705539e+00
## [391] -1.207721e-01 -5.019404e-01 -1.333490e+00 1.230895e+00 -1.053538e+00
## [396] 6.787876e-01 -7.735239e-02 -1.390559e+00 9.882291e-01 -1.200309e-01
## [401] 4.440402e-01 8.079128e-01 -3.495216e-02 6.406536e-01 -5.452836e-01
## [406] 1.388698e+00 -9.904421e-01 -4.207990e-01 4.774721e-01 -7.939384e-01
## [411] 1.344242e+00 -7.573188e-01 -1.026023e-01 -4.103529e-01 -1.101576e+00
## [416] 8.010501e-01 -1.097187e+00 1.489592e+00 -8.066983e-01 6.018070e-01
## [421] 1.132010e+00 -7.253453e-01 1.823648e+00 -6.030972e-01 8.124645e-01
## [426] 5.835517e-01 -9.374014e-01 1.510087e+00 -1.018166e+00 1.206018e+00
## [431] -1.001594e+00 -2.773291e-01 -3.730321e-01 -1.672272e+00 -6.880422e-02
## [436] -4.205412e-01 1.320823e+00 4.760875e-01 -6.560673e-01 4.411128e-01
## [441] -8.803951e-01 1.529648e+00 -8.466504e-01 2.909459e-01 1.311692e+00
## [446] -1.193525e+00 1.012512e+00 9.500088e-01 -3.640953e-01 2.046723e+00
## [451] -1.145893e+00 2.640795e-02 -1.469691e+00 7.740051e-01 -5.752697e-01
## [456] -5.432679e-01 8.833927e-01 -8.520489e-01 1.009406e+00 -1.162660e+00
## [461] -2.794290e-01 5.005443e-01 -1.426313e+00 1.588821e+00 -1.192371e+00
## [466] 7.254978e-01 -1.096278e+00 -1.348786e-01 1.333367e+00 -1.147409e+00
## [471] 1.570155e+00 -4.328085e-01 6.572186e-02 1.331640e+00 -2.074670e+00
## [476] -2.243994e+00 3.407715e+00 1.214725e+00 -6.945510e-01 3.073745e-01
## [481] 7.254490e-01 -8.829559e-01 9.117486e-01 -9.199603e-01 6.788146e-01
## [486] 1.322056e+00 -1.346823e+00 -4.614763e-01 -1.471834e+00 8.120091e-01
## [491] -6.323174e-01 -6.125849e-02 2.938798e-01 -1.236244e+00 8.857625e-01
## [496] -1.032401e-01 -1.123233e-01 1.347437e+00 -1.570300e+00 3.746275e-01
## [501] -1.175722e+00 9.543222e-01 -7.361703e-01 -6.042322e-01 7.236148e-01
## [506] -9.724933e-01 1.624762e+00 -8.670920e-02 4.281116e-01 2.797390e+00
## [511] -1.354073e+00 9.507271e-01 -5.959897e-01 9.440684e-01 -5.169391e-01
## [516] 1.746382e+00 1.579388e+00 -1.141588e+00 5.795251e-01 -1.721499e-01
## [521] -2.635213e-01 9.581559e-01 -1.142045e+00 1.381612e+00 -1.216951e+00
## [526] 7.030053e-01 -9.579224e-01 -3.518339e-02 -5.393065e-01 -1.061999e+00
## [531] 5.813169e-01 -5.366147e-01 -2.178545e-02 1.334448e+00 -1.398034e+00
## [536] 1.308380e+00 -1.153190e+00 9.342603e-01 -7.717358e-01 2.161237e-01
## [541] 1.268795e+00 -8.763231e-01 6.017059e-01 -5.134743e-01 6.021855e-01
## [546] 1.262872e+00 -1.433191e+00 -2.109187e-01 -1.107630e+00 9.290302e-01
## [551] -8.464050e-01 1.152731e-01 -6.739219e-01 -1.082735e+00 4.789036e-01
## [556] -5.707064e-01 5.751480e-01 4.921499e-01 -1.576431e+00 9.191196e-01
## [561] -9.200811e-01 8.762314e-01 -7.541119e-01 -8.396499e-01 6.307749e-01
## [566] -8.275212e-01 6.157874e-01 1.113748e+00 -7.202346e-01 1.520139e+00
## [571] -1.943831e+00 -1.406661e+00 -7.347560e-01 9.253633e-01 -9.946005e-01
## [576] -3.940480e-01 -3.074557e-01 -4.023424e-01 2.141723e-01 -1.027464e+00
## [581] -9.874246e-01 -7.961234e-01 -1.788263e+00 1.670084e+00 -5.740904e-01
## [586] 1.671005e-01 -1.212953e+00 1.510707e+00 1.418553e+00 -1.047851e+00
## [591] 1.854093e+00 -5.283516e-01 1.498588e+00 1.956567e+00 -2.354085e+00
## [596] -1.577275e+00 2.805399e+00 1.353952e+00 -1.206091e+00 9.286747e-01
## [601] 1.007990e+00 -4.095672e-01 1.239354e+00 -1.009968e+00 1.203554e+00
## [606] 9.828548e-01 -7.513329e-01 -5.972829e-01 -8.810379e-01 6.327317e-01
## [611] -8.040696e-01 3.650135e-01 7.005808e-01 -9.195253e-01 9.996987e-01
## [616] -4.029681e-01 3.480667e-01 2.654191e+00 -1.304929e+00 4.263280e-01
## [621] -8.862172e-01 6.650155e-01 -1.986540e-01 1.707560e-02 4.608562e-01
## [626] -8.453343e-01 6.596195e-01 8.424116e-02 -4.783789e-01 1.254507e+00
## [631] -3.069399e-01 1.555662e+00 -1.104039e+00 1.190959e+00 -8.211907e-01
## [636] 1.992035e-01 7.846942e-01 -1.182525e+00 -1.029486e-01 -7.249006e-01
## [641] -4.007020e-01 1.391321e+00 -7.579694e-01 1.155918e-01 -1.137766e+00
## [646] 9.571818e-01 -1.045060e+00 4.794167e-01 -9.339558e-01 -5.357212e-01
## [651] 1.077792e+00 -6.369509e-01 -3.622332e-01 6.389658e-01 -1.002355e+00
## [656] 1.550726e+00 -1.739012e+00 8.391423e-01 -3.665329e-01 1.639209e-01
## [661] 1.352799e+00 -5.907340e-01 9.340068e-02 -5.804557e-01 8.445996e-01
## [666] 2.000555e+00 -9.333469e-01 -2.524190e-01 -9.259603e-01 7.757312e-01
## [671] -9.680013e-01 5.151838e-01 1.284505e+00 -7.998247e-01 1.338651e+00
## [676] -5.854399e-01 3.357788e-01 3.386391e-01 -1.138453e+00 5.123959e-01
## [681] -1.541208e+00 5.545474e-01 -6.605043e-01 -3.873343e-01 1.347371e-01
## [686] -7.284558e-01 4.404136e-01 3.153986e-01 -6.208946e-01 8.885422e-01
## [691] -7.269872e-01 -3.044192e-01 -1.145489e+00 1.371737e+00 -1.042768e+00
## [696] -7.489994e-01 -3.533364e-01 -5.823349e-01 9.606255e-01 -3.115176e-01
## [701] -4.417762e-01 -7.429553e-02 -4.551528e-01 1.460067e+00 -8.361915e-01
## [706] 1.213856e+00 -1.152548e+00 6.820813e-01 1.724694e+00 -1.751227e+00
## [711] 1.749717e+00 -2.008568e-01 2.547684e-03 6.918349e-01 -2.443315e+00
## [716] -1.762035e+00 3.700922e+00 1.059824e+00 -1.282265e+00 1.052026e+00
## [721] 5.261030e-01 -1.637784e+00 9.834018e-01 -6.680767e-01 -9.181923e-02
## [726] 1.667263e+00 -1.510914e+00 9.314448e-01 -9.458599e-01 1.260142e+00
## [731] -1.198707e+00 -1.813296e-01 1.529995e+00 -1.841488e+00 6.674217e-02
## [736] -8.852452e-01 3.259874e-01 7.704201e-01 -9.504009e-01 -3.379344e-01
## [741] -1.380050e+00 1.248111e+00 -9.615037e-01 2.423219e-01 2.008737e+00
## [746] -1.884554e+00 4.428296e-01 -2.233177e-01 2.310223e-01 2.268064e+00
## [751] -6.399836e-01 6.653492e-01 -1.456426e+00 1.365017e+00 -1.158145e+00
## [756] 1.307152e+00 3.232701e-01 -1.843904e+00 1.558030e+00 -1.076504e+00
## [761] 1.003143e-01 1.414055e+00 -5.258808e-01 9.865807e-01 -1.065085e+00
## [766] 1.214321e+00 -1.347369e+00 3.241514e-01 5.231314e-01 -1.656110e+00
## [771] 1.436689e+00 -8.500891e-01 -1.162852e-01 -4.367995e-01 -1.159924e+00
## [776] 4.266453e-01 -1.478766e+00 1.333328e+00 -9.104411e-01 2.897564e-01
## [781] 1.600475e+00 -1.651124e+00 1.942042e+00 -3.408496e-01 -1.821597e-01
## [786] 1.245976e+00 -8.196127e-01 1.083408e+00 -1.491340e+00 1.255513e+00
## [791] -1.460388e+00 6.319226e-01 8.373236e-01 -1.866299e+00 1.231762e+00
## [796] -7.168166e-01 4.163759e-01 6.049958e-01 -9.202730e-01 7.527035e-01
## [801] -1.342048e+00 1.345187e+00 -1.389757e+00 -8.547777e-01 1.221752e+00
## [806] -1.753724e+00 1.656499e+00 5.256378e-01 -7.035827e-01 2.131680e+00
## [811] -6.823770e-01 2.161324e-01 -8.571315e-01 3.328836e-01 -4.298182e-01
## [816] -1.399539e-01 -9.734002e-02 1.987950e-01 1.482170e-01 1.015217e-02
## [821] 3.193759e-01 4.158293e-01 -8.236813e-01 6.792259e-01 -7.644525e-01
## [826] 5.016962e-01 -2.832353e-01 3.503744e-02 2.399446e-03 9.726505e-02
## [831] 1.515158e-01 -8.287266e-02 2.075058e-01 1.577335e+00 -7.434164e-01
## [836] -1.462939e+00 1.222732e+00 3.109401e-01 -3.462610e-01 3.187216e-01
## [841] 9.832440e-03 4.100475e-03 -2.335042e-02 4.010991e-02 5.701002e-01
## [846] 2.761767e-01 -9.992421e-01 4.431770e-01 -7.731200e-01 5.028032e-01
## [851] -4.078195e-01 1.045416e+00 -2.634835e-02 -3.458596e-02 -1.061173e-01
## [856] -1.193450e-01 3.350034e-01 3.867053e-01 -7.507679e-01 -8.952476e-02
## [861] -8.739218e-01 4.698740e-01 -4.998097e-01 1.900160e-01 1.425112e-01
## [866] 5.756099e-02 -6.958115e-02 -1.815593e-01 2.198442e-01 -1.385758e-01
## [871] -8.644261e-01 1.167373e+00 -7.302359e-01 6.387838e-01 -3.904960e-01
## [876] -3.170935e-01 -1.377087e-01 5.172864e-02 1.743614e-01 -1.591813e-01
## [881] -3.817584e-01 -7.822468e-02 -9.850639e-01 4.840461e-01 -8.385714e-01
## [886] 6.541890e-01 -5.411145e-01 5.532908e-01 2.971384e-01 8.746454e-02
## [891] 1.353822e-01 -2.714385e-01 8.940436e-01 1.017339e+00 -1.029644e+00
## [896] 1.828434e-01 -6.735175e-01 4.701865e-01 -4.403052e-01 8.362105e-01
## [901] -2.079224e-01 4.618486e-04 3.645933e-02 -5.810865e-02 -2.869209e-01
## [906] 3.498472e-01 -9.246504e-01 1.670561e-01 -5.288251e-01 5.789651e-01
## [911] -3.795396e-01 2.030309e-02 -3.608280e-02 1.669532e-01 3.737987e-02
## [916] -1.260736e-01 1.053061e-01 1.091631e+00 -9.117740e-01 7.715747e-01
## [921] -5.635743e-01 6.771384e-01 -3.984844e-01 7.455485e-01 1.818994e-01
## [926] 1.226622e-01 2.071885e-01 -2.051015e-01 -1.007377e-01 1.420001e+00
## [931] -6.017203e-01 1.098954e-01 4.070173e-01 4.491797e-01 -1.563580e-01
## [936] -6.351712e-01 -1.264425e-01 3.880596e+00 -6.576296e-01 2.610120e-01
## [941] -9.362322e-01 -4.370287e-01 4.407421e-01 -1.341554e+00 -5.098334e-01
## [946] -8.759394e-01 -4.482729e-01 3.564811e+00 -2.750700e-01 1.410491e+00
## [951] 2.883292e-01 -2.691633e+00 -4.489534e-01 -7.369614e-01 -2.705284e-01
## [956] -6.545071e-01 3.956825e-01 -6.165742e-01 -1.448232e-01 8.316808e-01
## [961] -6.496999e-01 -7.281815e-01 -1.683026e-01 -1.356064e+00 3.638206e-01
## [966] -5.126943e-01 1.517099e-01 -1.775546e-01 1.744150e-01 2.113990e-01
## [971] -6.133002e-01 1.319017e+00 6.419010e-02 -9.194823e-01 1.212081e+00
## [976] -1.655742e-01 3.902230e-01 -3.651101e-01 -1.056193e-01 5.792005e-01
## [981] -5.143425e-01 -2.854607e-02 5.420836e-02 -6.310794e-01 9.395378e-01
## [986] -1.991450e-01 4.579619e-01 -8.761570e-02 2.875274e-02 6.970465e-01
## [991] -6.228886e-01 -1.959972e-01 1.216406e-01 -2.147757e-01 -4.184426e-01
## [996] -4.898492e-01 8.697504e-02 -3.608926e-01 2.411700e-01 1.453832e+00
## [1001] -6.535854e-01 5.766083e-01 1.575804e-01 1.997338e-01 6.091246e-01
## [1006] -4.873119e-01 1.925171e-01 -2.059612e-01 4.342973e-02 1.433101e+00
## [1011] -5.522658e-01 -7.130617e-01 2.383787e-01 -1.747323e-01 8.642898e-01
## [1016] -4.275207e-01 3.301673e-01 -2.061229e-01 -2.298828e-03 7.017249e-01
## [1021] -6.214240e-01 -4.815987e-01 2.499195e-01 -6.952621e-01 2.577253e-02
## [1026] -3.845445e-01 5.559705e-01 -5.392631e-02 9.709768e-02 8.947195e-01
## [1031] -3.477333e-01 3.186642e-02 -5.892808e-01 3.005019e-01 -2.130752e-01
## [1036] -1.090961e-01 -4.398570e-02 4.181378e-02 -8.052684e-03 1.362619e-01
## [1041] 1.474965e-01 3.865951e-01 -6.047289e-01 7.305050e-01 -3.388306e-01
## [1046] 2.533080e-01 7.078886e-02 8.916814e-02 7.544798e-02 7.972831e-02
## [1051] 1.736433e-01 -1.038008e-01 3.220800e-01 1.156435e+00 -4.201301e-01
## [1056] -1.165305e+00 6.276482e-01 5.640114e-01 -3.065693e-01 4.168301e-01
## [1061] 1.837259e-01 -9.230643e-02 -1.957242e-01 5.022154e-03 -5.495033e-02
## [1066] -1.510566e-01 -7.407158e-01 1.363773e-01 -5.178468e-01 1.415863e-01
## [1071] -1.063116e-01 7.412230e-01 2.660474e-02 -1.321283e-01 -2.279723e-01
## [1076] -1.728002e-01 1.804285e-01 2.837023e-01 -4.179243e-01 -2.015589e-01
## [1081] -7.163989e-01 2.784566e-01 -3.229979e-01 -9.337946e-02 1.257643e-02
## [1086] 1.006386e-01 -1.776925e-01 -3.905977e-02 1.635052e-01 3.729457e-02
## [1091] -4.506937e-01 3.749758e-01 -5.104003e-01 3.911737e-01 -1.910712e-01
## [1096] -3.173549e-01 -2.466674e-01 2.337396e-02 2.591464e-01 -4.235308e-02
## [1101] -5.017812e-02 -1.655556e-01 -4.426044e-01 4.617235e-01 -5.238667e-01
## [1106] 2.805803e-01 -2.227405e-01 4.431390e-01 6.729039e-01 1.697126e-01
## [1111] 1.628665e-01 -2.977658e-01 4.745907e-01 5.101125e-01 -7.818161e-01
## [1116] 3.163858e-02 -3.616161e-01 1.935864e-01 -3.451819e-01 5.697755e-01
## [1121] 6.366188e-03 7.660635e-03 2.407644e-02 -3.408158e-02 -1.572765e-01
## [1126] 4.724474e-01 -7.208653e-01 4.476960e-01 -4.418242e-01 3.155649e-01
## [1131] -3.008623e-01 4.618802e-02 7.187652e-02 1.588220e-01 1.894930e-02
## [1136] 6.211559e-02 2.796233e-01 6.868759e-01 -7.077405e-01 3.743828e-01
## [1141] -3.334698e-01 4.479773e-01 1.414969e-02 7.672993e-02 1.796988e-01
## [1146] 1.189844e-01 1.420164e-01 -1.447799e-01 -4.152994e-01 1.090449e+00
## [1151] -2.085151e+00 1.275426e-02 -1.187238e+00 7.258823e-01 -1.114377e+00
## [1156] 1.419141e-01 2.163012e-03 7.735780e-02 3.855374e-01 -1.086403e+00
## [1161] -7.636226e-01 4.318274e-01 -1.211681e+00 6.874318e-01 -7.682221e-01
## [1166] 3.618005e-01 -1.343454e+00 1.679022e+00 1.242944e+00 -1.543538e+00
## [1171] 2.108208e+00 -2.208006e-01 1.493816e+00 1.800281e+00 -2.622237e+00
## [1176] -1.511841e+00 3.076339e+00 1.091901e+00 -1.362670e+00 6.473341e-01
## [1181] 4.877857e-01 -1.550825e-01 1.499787e+00 -1.244065e+00 5.465526e-01
## [1186] 7.874071e-01 -9.523858e-01 -1.181393e+00 -5.438297e-01 4.732867e-01
## [1191] -1.371564e+00 6.552994e-01 6.641445e-01 -1.451469e+00 5.388873e-01
## [1196] -2.167712e-02 4.232900e-01 1.458110e+00 -1.393271e+00 1.142168e+00
## [1201] -1.067266e+00 9.092398e-01 -1.032037e+00 -1.060766e+00 2.006641e+00
## [1206] -1.447908e+00 5.969262e-02 -3.105739e-01 1.480730e-01 1.263937e+00
## [1211] -5.381894e-01 8.260310e-01 -1.150323e+00 8.916295e-01 -1.051857e+00
## [1216] -4.710792e-02 5.385003e-01 -1.337753e+00 -4.416074e-01 -1.199807e-01
## [1221] -3.278732e-01 1.661117e+00 -8.998514e-01 1.188696e+00 -7.792588e-01
## [1226] 6.871495e-01 -5.378827e-01 9.465837e-01 -1.031399e+00 -6.462986e-02
## [1231] 6.313509e-01 -5.673610e-01 -3.232602e-01 3.098350e-01 -1.200899e+00
## [1236] 2.123102e+00 -1.482862e+00 7.050228e-01 -3.944695e-01 1.424816e-01
## [1241] 7.126116e-01 -3.821803e-01 1.103007e+00 -3.564584e-01 7.796569e-01
## [1246] 2.899450e+00 4.000134e-02 -3.052604e-01 -5.943978e-01 8.442950e-01
## [1251] -9.392562e-01 5.294552e-01 6.290884e-01 -9.287511e-01 1.953646e+00
## [1256] -8.232940e-01 -7.617496e-02 6.640626e-03 -4.104371e-01 6.452829e-01
## [1261] -1.185321e+00 7.129043e-01 -1.050578e+00 -3.271227e-01 -4.094805e-01
## [1266] -1.154428e+00 1.260186e-01 2.131004e-02 -4.971726e-01 9.396830e-01
## [1271] -6.552083e-01 7.174913e-01 -9.810657e-01 3.239926e-01 -5.343882e-01
## [1276] -5.402903e-02 -4.608486e-01 -3.360373e-02 -3.539780e-02 3.341027e-01
## [1281] 4.545633e-01 7.703386e-01 -8.869407e-01 6.644998e-01 -5.862720e-01
## [1286] 4.889835e-01 -1.733693e-01 5.566814e-02 -2.343007e-01 1.312742e-01
## [1291] 2.133115e-01 -8.172409e-02 3.318347e-01 1.333982e+00 -6.561357e-01
## [1296] -1.504576e+00 7.201687e-01 7.666728e-01 -4.140038e-01 4.525762e-01
## [1301] 3.220561e-02 -8.068526e-02 -1.564082e-01 3.265808e-01 4.618868e-01
## [1306] 9.088253e-02 -9.438816e-01 3.349692e-02 -7.312629e-01 5.584081e-01
## [1311] -3.173452e-01 8.975786e-01 1.477081e-01 -7.160807e-02 -1.440548e-01
## [1316] -2.263799e-01 2.864293e-01 4.707434e-01 -6.246476e-01 -3.138484e-01
## [1321] -7.840566e-01 6.972494e-01 -5.003169e-01 -2.170620e-01 4.874379e-02
## [1326] -8.191679e-03 -6.037755e-02 -1.867729e-01 2.445160e-01 -3.351599e-01
## [1331] -6.999442e-01 1.004884e+00 -5.102877e-01 7.279793e-01 -3.523053e-01
## [1336] -2.831143e-01 -4.132332e-01 1.565547e-01 2.837770e-01 -1.874612e-01
## [1341] -1.434588e-01 4.691809e-02 -9.695107e-01 3.107976e-01 -6.550737e-01
## [1346] 4.884320e-01 -5.931247e-01 3.681878e-01 3.628861e-01 2.667045e-02
## [1351] 2.421630e-01 -3.766495e-01 8.366305e-01 6.996241e-01 -1.030573e+00
## [1356] 8.644129e-02 -6.180118e-01 4.277849e-01 -3.514276e-01 1.159951e+00
## [1361] -1.120490e-01 5.649760e-02 7.397534e-02 2.605206e-03 -9.434822e-02
## [1366] 4.822387e-01 -9.663911e-01 1.497120e-01 -5.870366e-01 5.792824e-01
## [1371] -3.450197e-01 -8.160255e-02 -1.311256e-01 1.569621e-01 -1.120999e-02
## [1376] -4.883568e-02 3.567826e-01 1.043547e+00 -1.003665e+00 7.034816e-01
## [1381] -2.028425e-01 8.070189e-01 -2.231263e-01 1.973585e-01 1.642301e-01
## [1386] 5.397111e-02 2.067308e-01 -2.794689e-01 -4.520524e-01 1.635771e+00
## [1391] -9.062465e-01 -4.150949e-01 -1.023887e+00 5.821678e-01 -6.195839e-01
## [1396] -4.332162e-01 1.243254e+00 -4.168729e-01 2.910097e-01 -1.049288e+00
## [1401] -5.774533e-01 7.289856e-01 -1.527417e+00 1.962187e-01 3.729892e-04
## [1406] 6.117945e-01 -7.351952e-01 3.778681e-01 8.181244e-01 -9.349427e-01
## [1411] 1.100627e+00 -2.296217e-01 7.765240e-01 1.370305e+00 -1.913333e+00
## [1416] -1.405239e+00 1.859840e+00 1.231510e+00 -4.903691e-01 -1.005339e-01
## [1421] 2.503144e-01 -5.565405e-01 8.386786e-01 -4.685320e-01 5.682040e-01
## [1426] 7.148544e-01 -1.259841e+00 -2.998315e-01 -1.079829e+00 6.044279e-01
## [1431] -5.803216e-01 -3.947168e-01 4.127652e-01 -8.567464e-01 5.554799e-01
## [1436] 2.865498e-01 5.440536e-01 1.407143e+00 -9.073548e-01 1.543652e-01
## [1441] -3.113273e-01 9.394222e-01 -3.871635e-01 -1.005826e-01 -7.085339e-02
## [1446] -7.568577e-01 3.923134e-01 3.004455e-01 -1.163470e-01 1.565375e+00
## [1451] -1.404989e-01 4.107940e-01 -4.934614e-01 8.013326e-01 -1.562181e-01
## [1456] 3.789108e-01 6.061238e-01 -7.973720e-01 1.437403e-01 -1.614240e-01
## [1461] 1.345284e-01 1.122838e+00 -5.049004e-01 -2.761826e-01 -5.063333e-01
## [1466] 1.081786e+00 -4.405607e-01 -5.177275e-01 -1.474053e-02 -2.600735e-01
## [1471] 6.738761e-01 -4.267542e-01 -5.134789e-01 7.161332e-01 -9.055226e-01
## [1476] 2.409194e-01 -1.006397e+00 1.070317e+00 -1.751608e-01 -6.922600e-01
## [1481] 8.309425e-01 -3.689648e-01 3.998111e-01 -1.041186e-01 8.689974e-01
## [1486] 1.508156e+00 -1.347804e+00 -9.853598e-01 -4.307880e-01 9.521626e-01
## [1491] -4.889071e-01 3.916135e-02 1.459220e-02 -6.690566e-01 5.727474e-01
## [1496] -7.624518e-01 1.233339e-01 2.531109e-01 -1.202452e+00 -4.975706e-02
## [1501] -8.494489e-01 9.801599e-01 -5.607874e-01 -6.424111e-01 -1.548987e-01
## [1506] -6.603101e-01 4.806692e-01 3.986834e-01 -7.637544e-01 8.968064e-01
## [1511] -5.260902e-01 1.050561e-01 3.525040e+00 1.141091e-01 6.879548e-02
## [1516] 1.572289e-01 -9.156180e-02 -2.953482e-01 1.869637e-02 -8.636722e-01
## [1521] -6.381193e-01 5.650684e-01 -1.195604e+00 2.275724e-01 4.471497e+00
## [1526] 1.160490e-01 4.053028e-01 -4.285739e-01 -2.895568e-01 -9.187350e-01
## [1531] -3.661321e-01 -7.948486e-01 -2.032516e-01 -4.458029e-02 -1.031307e+00
## [1536] -1.960821e+00 2.119161e-01 -8.129544e-02 8.974113e-01 -4.515639e-01
## [1541] 3.841166e-01 -8.371436e-01 -2.931916e-01 -4.042162e-01 1.243190e-01
## [1546] 5.507809e-01 -9.160757e-01 1.014266e-01 2.256513e-01 4.595584e-01
## [1551] -6.703402e-01 5.361065e-01 -4.221347e-01 -6.717750e-01 2.776913e-01
## [1556] -2.151910e-01 8.577839e-01 2.839415e-01 -6.958971e-01 2.690125e-01
## [1561] -1.012664e+00 6.503858e-01 -6.319782e-01 -6.132854e-01 8.695331e-01
## [1566] -4.255896e-01 1.656896e-01 -1.328588e-01 2.618043e-01 2.128974e-01
## [1571] -8.202215e-01 1.886168e-01 -8.802045e-01 7.424459e-01 -4.170920e-01
## [1576] -5.089099e-01 8.577614e-01 -4.582990e-01 6.072305e-01 -1.568704e-01
## [1581] 3.394932e-01 8.484665e-03 -7.551686e-01 2.806383e-01 -8.206688e-01
## [1586] 8.725785e-01 -4.874147e-01 2.098165e-01 6.382577e-01 -3.952994e-01
## [1591] 3.119409e-01 -1.030005e-01 5.822829e-01 5.542897e-01 -7.429129e-01
## [1596] 6.660233e-01 -9.209426e-01 7.988880e-01 -3.286550e-01 -5.779734e-01
## [1601] 4.227667e-02 -4.341058e-01 4.866313e-01 -8.682015e-02 -2.530331e-01
## [1606] 8.432390e-02 -8.763014e-01 4.246463e-01 -8.367643e-01 9.064631e-01
## [1611] -3.718452e-01 6.154533e-01 3.657957e-01 -3.756216e-01 6.277039e-01
## [1616] -1.330564e-01 6.051927e-01 4.690371e-01 -8.911159e-01 1.745606e-01
## [1621] -6.823359e-01 9.140709e-01 -4.084215e-01 8.140663e-01 1.935137e-02
## [1626] -3.831318e-01 4.362814e-01 -3.216952e-02 2.823295e-03 4.733856e-01
## [1631] 3.200141e-01 1.758177e-02 -1.076259e+00 7.561643e-01 -5.521783e-01
## [1636] -1.398032e-01 9.166511e-01 -2.708170e-01 1.051335e+00 -1.347391e+00
## [1641] -5.689927e-01 9.014690e-01 -1.263603e+00 2.182953e-01 -7.431595e-01
## [1646] 2.834185e-01 -7.607949e-01 1.283491e-03 2.830408e-01 -6.991549e-01
## [1651] -9.330888e-02 -9.328618e-02 9.017550e-01 6.561494e-01 -1.214299e+00
## [1656] -7.146653e-01 8.835024e-01 4.904313e-01 -4.755197e-01 1.116930e+00
## [1661] 8.197494e-01 -1.082642e-01 5.935710e-01 -9.028830e-01 -5.175651e-02
## [1666] 8.587547e-01 -1.864423e-01 3.620952e-01 -8.780635e-01 5.244552e-01
## [1671] -6.616106e-01 -2.939994e-01 1.036850e+00 -5.721652e-01 1.171750e+00
## [1676] -3.586302e-01 -2.652764e-01 1.125822e+00 -9.436873e-01 1.243854e-02
## [1681] -4.420257e-01 3.870034e-01 -5.600218e-01 6.576246e-02 -6.941256e-01
## [1686] -4.686689e-01 1.213375e+00 -5.386516e-01 3.651628e-03 9.003059e-02
## [1691] -1.094562e+00 1.943817e-01 -4.674897e-01 5.756392e-01 -4.628134e-01
## [1696] 4.809366e-01 8.280310e-01 -6.465932e-01 5.007873e-01 -2.591762e-01
## [1701] -1.189211e-01 4.835107e-01 -2.188730e-01 -3.408758e-01 -4.639766e-01
## [1706] 7.453400e-01 -3.015786e-02 -3.651187e-02 6.391858e-01 -5.192147e-01
## [1711] 1.113863e+00 4.062463e-01 -1.256116e-01 6.397624e-01 -7.862181e-01
## [1716] 1.963342e-01 -5.313052e-01 7.232460e-01 -4.418981e-01 -2.148222e-01
## [1721] 3.112899e-01 -3.323113e-01 4.613649e-01 -4.247811e-01 7.065196e-02
## [1726] 4.542169e-01 -1.031483e+00 -5.050539e-01 -4.078954e-01 6.888807e-01
## [1731] -5.708169e-01 4.247241e-01 -2.697933e-01 -5.026983e-01 4.251388e-02
## [1736] -4.453136e-01 4.164949e-01 6.611049e-01 -1.188899e-01 9.598639e-02
## [1741] -6.789208e-01 6.396431e-01 -1.657036e-02 4.790070e-02 5.325752e-01
## [1746] -3.221795e-01 1.185691e+00 8.032084e-03 -1.069984e+00 1.196549e+00
## [1751] -1.230530e+00 4.470535e-01 -1.339937e+00 9.348469e-01 -1.551865e+00
## [1756] -5.912366e-01 1.382962e-03 -1.106526e+00 2.585807e-02 -5.973282e-01
## [1761] -9.136352e-02 2.976050e-01 -6.681505e-01 3.311873e+00 -1.197539e+00
## [1766] 1.174007e+00 -9.118193e-01 1.492463e+00 7.161127e-01 -8.529367e-01
## [1771] 1.211023e+00 -1.546294e-01 4.955466e-01 1.842879e+00 -1.689991e+00
## [1776] -2.046526e+00 1.856584e+00 7.120044e-01 -8.432329e-01 1.750453e+00
## [1781] 9.115201e-01 -8.228851e-01 1.377260e+00 -3.683746e-01 -4.215291e-01
## [1786] 5.851584e-01 -9.385300e-01 7.198709e-01 -1.144016e+00 1.007859e+00
## [1791] -3.680355e-01 -2.643552e-01 2.670309e-01 -8.361050e-01 9.991828e-01
## [1796] -2.137761e-01 6.336426e-01 -4.303620e-01 -9.272251e-01 -3.681242e-02
## [1801] -1.606371e+00 9.350285e-01 -1.212093e+00 -4.632019e-01 3.425631e-01
## [1806] -1.057234e+00 2.126907e-01 1.857594e-01 2.132155e-01 -3.108545e-01
## [1811] -8.196039e-01 3.604762e-01 -1.494285e+00 1.172565e+00 -1.512693e+00
## [1816] -5.980345e-02 3.911147e-01 -1.019963e+00 8.379559e-01 -1.095310e+00
## [1821] 8.819189e-01 4.250522e-01 8.858955e-02 9.797265e-01 -9.263054e-01
## [1826] 1.114698e+00 -1.409872e+00 1.466554e+00 1.284340e+00 -1.127024e+00
## [1831] 7.235289e-01 -9.732974e-01 8.022771e-01 1.004226e+00 -1.028498e+00
## [1836] -5.072518e-01 -1.540605e+00 1.171021e+00 -1.013545e+00 2.076348e+00
## [1841] 1.516763e+00 -1.114218e+00 1.077478e+00 -8.065814e-01 6.719601e-01
## [1846] 2.231404e-01 -1.717726e+00 1.491018e+00 -1.270852e+00 1.092543e+00
## [1851] -1.221176e+00 -6.457020e-01 8.292016e-01 -8.656186e-01 1.569055e+00
## [1856] -7.182784e-01 9.180792e-01 8.238474e-01 -1.220126e+00 1.477491e-01
## [1861] -9.472157e-01 1.231845e+00 -1.000448e+00 2.188504e-01 7.091291e-02
## [1866] -9.610655e-01 3.263296e-01 9.513573e-01 -9.546507e-01 2.337611e+00
## [1871] -9.620619e-01 3.891782e-01 -1.331435e+00 6.977359e-01 -6.191447e-01
## [1876] 9.954805e-01 1.707784e+00 -2.389192e-01 8.942136e-01 -1.311222e+00
## [1881] -6.328881e-01 1.607313e+00 -2.028263e+00 2.574838e-02 -8.600259e-01
## [1886] 5.926155e-01 -1.070618e+00 6.194293e-01 7.807353e-01 -1.103883e+00
## [1891] 7.474208e-01 -4.838742e-01 9.618925e-01 1.164610e+00 -2.022540e+00
## [1896] -1.604176e+00 1.982836e+00 9.040349e-01 -7.647447e-01 3.010431e-01
## [1901] 6.759678e-01 -5.381230e-01 1.020662e+00 -7.671043e-01 -5.589825e-02
## [1906] 4.691376e-01 -1.047029e+00 -5.762916e-01 -1.031157e+00 8.728364e-01
## [1911] -7.745756e-01 -2.836868e-01 2.842121e-01 -9.187366e-01 4.259259e-01
## [1916] -3.554116e-01 2.915330e-01 1.813791e+00 -1.424487e+00 4.805174e-01
## [1921] -5.219574e-01 8.870547e-01 -4.748443e-01 -5.390086e-01 5.121005e-01
## [1926] -8.079390e-01 2.963403e-01 8.392327e-02 1.605797e-03 2.329790e-01
## [1931] -8.796395e-01 9.551551e-02 -6.601834e-01 1.002358e+00 -6.423291e-01
## [1936] 3.526997e-01 1.161841e+00 -6.600556e-01 -1.073328e-01 -7.159725e-03
## [1941] 1.948943e-01 6.408725e-01 -8.185122e-01 8.507307e-01 -6.460713e-01
## [1946] 1.360330e+00 -4.576615e-01 1.272312e-02 7.234565e-02 -9.105196e-02
## [1951] 7.187705e-01 -2.938008e-01 3.892975e-01 1.371217e+00 -1.007930e+00
## [1956] 6.987485e-01 -1.115380e+00 1.344984e+00 -1.521965e-01 -4.215723e-01
## [1961] 1.512992e-01 -2.952012e-01 7.228495e-01 -4.549567e-01 2.980620e-01
## [1966] 9.268902e-01 -9.182075e-01 -3.735943e-01 -3.794075e-01 1.190754e+00
## [1971] -6.047539e-01 4.407680e-01 -3.982174e-01 -5.029060e-01 4.233072e-01
## [1976] -2.870042e-01 3.496922e-02 6.564202e-01 -9.430369e-01 8.265138e-01
## [1981] -8.306936e-01 1.267555e+00 -5.540664e-01 -1.754171e-02 1.682227e-01
## [1986] -6.799600e-01 8.229808e-01 4.671185e-01 -3.993640e-01 8.903201e-01
## [1991] -1.321118e-02 -2.848243e-01 -4.472729e-01 2.879888e-01 2.074111e-01
## [1996] -5.210969e-01 -3.278931e-01 -3.931984e-01 -9.587463e-02 -1.235521e-01
## [2001] -2.291159e-01 2.408660e-02 1.082072e-01 -7.455315e-02 -3.463380e-01
## [2006] 2.281937e-01 -3.621014e-01 2.709643e-02 9.221875e-02 -1.919459e-01
## [2011] 7.883169e-01 -2.893248e-02 1.964095e-01 8.058143e-01 4.040914e-02
## [2016] -6.893457e-01 8.708777e-01 1.660454e-01 -1.509079e-01 4.531970e-01
## [2021] -5.779676e-01 -2.614993e-01 4.438001e-01 -2.858229e-01 -3.873755e-01
## [2026] 1.055597e+00 -2.992881e-01 1.512116e+00 -3.085336e-01 9.055370e-02
## [2031] -2.166596e-01 -7.497652e-02 -2.612666e-01 -4.596359e-01 -3.806865e-02
## [2036] -1.808028e-01 6.638283e-02 -5.116563e-02 -5.859696e-01 5.796391e-01
## [2041] -3.479876e-01 3.464275e-01 -3.833272e-01 -9.789691e-01 1.347443e-01
## [2046] -2.428729e-01 2.056144e-01 -1.564163e-01 1.981952e-01 1.957505e-01
## [2051] 1.221552e-01 2.571000e-01 -3.259016e-01 3.455576e-01 8.793380e-03
## [2056] 4.340341e-01 5.479976e-01 -3.309442e-01 5.325979e-01 -3.383251e-01
## [2061] 6.847158e-02 2.378522e-01 -2.578718e-02 -7.764791e-02 1.970943e-01
## [2066] 3.154403e-01 5.909588e-02 -3.154342e-01 -2.422696e-01 -1.219369e-01
## [2071] 1.558840e-01 6.232832e-02 -3.425422e-01 -1.663880e-01 1.818590e-01
## [2076] 9.567862e-02 -3.932149e-01 6.520720e-01 2.083967e-01 -4.314575e-01
## [2081] -3.738111e-01 -2.905116e-01 4.669865e-01 -1.418487e-01 -5.197754e-02
## [2086] -1.422996e-01 -1.605384e-01 6.290952e-02 1.643477e-01 6.460172e-01
## [2091] -3.551213e-02 -1.494108e-01 -5.968589e-01 -1.998090e-01 6.289584e-01
## [2096] 7.491139e-02 1.028266e-03 -5.246055e-01 -2.553629e-01 -5.413126e-01
## [2101] 5.443061e-02 5.221673e-01 -2.026242e-01 -9.251677e-01 -8.977813e-02
## [2106] -2.629706e-01 5.056361e-02 1.922657e-01 -1.499261e-01 6.786984e-02
## [2111] -1.750885e-01 9.625971e-02 -1.185070e+00 6.391563e-01 -1.150356e+00
## [2116] -5.708817e-01 8.494404e-01 -4.830326e-01 -1.173779e-01 -2.951043e-02
## [2121] -4.188187e-01 -5.097843e-01 -1.219133e+00 -6.995867e-01 -1.254361e+00
## [2126] 1.265292e+00 -4.187548e-01 3.561470e-01 -2.455517e-01 -7.890512e-01
## [2131] 7.136981e-01 -3.823860e-01 2.113677e-01 1.199790e+00 -1.293438e+00
## [2136] -9.865255e-01 3.033169e+00 -1.604743e-01 -1.592572e+00 7.039321e-01
## [2141] 7.828854e-01 -9.246455e-01 2.478105e-01 -5.440859e-02 1.305070e+00
## [2146] 1.852809e+00 -2.004221e+00 1.123533e+00 -1.591942e+00 2.329907e+00
## [2151] -9.736130e-01 1.031289e+00 1.821735e+00 -1.457440e+00 1.898407e-01
## [2156] 6.674300e-01 -5.536361e-01 1.347364e+00 6.967066e-01 3.447402e-01
## [2161] -1.330697e+00 6.281995e-01 -1.855955e+00 8.714966e-01 1.364347e+00
## [2166] -7.628634e-01 6.761586e-01 -6.791142e-01 -4.027061e-01 1.988936e-01
## [2171] -1.007499e+00 1.483246e+00 -1.126803e+00 3.161142e+00 -9.323560e-01
## [2176] 7.533175e-01 -6.280943e-01 -2.825944e-01 -6.835839e-02 -4.666479e-01
## [2181] -1.137522e+00 1.297522e+00 -1.199288e+00 2.614036e+00 -1.889146e+00
## [2186] 2.149003e+00 -1.795114e+00 3.028145e-01 1.052131e+00 -7.073651e-01
## [2191] 1.134297e+00 -1.620208e+00 1.138318e+00 1.956917e+00 -1.311369e+00
## [2196] 1.830277e-02 -1.325082e+00 -1.495892e-01 -5.767032e-01 -5.869934e-02
## [2201] -1.301650e+00 -9.584963e-01 7.879289e-01 2.642733e-01 2.215387e-03
## [2206] 2.685049e-01 -1.640090e+00 -3.746798e-01 -1.166959e+00 9.182201e-01
## [2211] -1.023029e+00 8.883604e-01 7.053010e-03 -1.190271e+00 -3.362497e-01
## [2216] -4.643873e-01 -1.570090e-01 1.803333e+00 3.059677e-01 -1.510179e-01
## [2221] 2.167640e-01 1.362257e+00 1.016220e-01 1.853727e+00 9.716260e-01
## [2226] -3.038465e-01 1.336438e+00 -8.331813e-01 3.575019e-01 8.158242e-01
## [2231] -1.070842e+00 4.513916e-01 -9.049207e-01 7.685280e-01 -7.059913e-01
## [2236] -3.752913e-01 -3.428669e-01 -2.077532e-02 -2.416559e-02 8.589276e-02
## [2241] 5.542683e-01 6.028420e-01 -1.212882e+00 9.868128e-01 -7.393456e-01
## [2246] 6.242160e-01 -2.429155e-01 -8.622874e-02 -8.706669e-02 -3.113766e-02
## [2251] 1.662326e-02 -1.761513e-01 7.433913e-02 1.988189e+00 -1.161609e+00
## [2256] -1.908783e+00 1.119369e+00 9.572522e-01 -5.321065e-01 3.401768e-01
## [2261] 6.290310e-02 -1.120411e-01 -1.895898e-01 2.998223e-01 1.399027e+00
## [2266] 2.192277e-01 -1.313202e+00 4.135820e-01 -8.550012e-01 8.017127e-01
## [2271] -4.682698e-01 1.120143e+00 1.491188e-01 -2.322651e-01 -3.043710e-01
## [2276] 5.832657e-02 3.393348e-01 4.628740e-01 -6.575068e-01 -2.011294e-01
## [2281] -8.904297e-01 8.691315e-01 -6.053237e-01 1.126596e-01 1.482304e-01
## [2286] 5.419687e-02 -7.069184e-02 -2.302292e-01 4.826560e-01 -1.723551e-01
## [2291] -9.477330e-01 1.970404e+00 -7.507163e-01 9.223183e-01 -4.309636e-01
## [2296] -3.783886e-01 -3.314181e-01 7.116558e-03 3.509666e-01 -1.527890e-01
## [2301] -1.521890e-01 -4.778220e-02 -1.273377e+00 6.457321e-01 -9.380224e-01
## [2306] 7.561419e-01 -6.247667e-01 7.107968e-01 3.148638e-01 -1.648491e-02
## [2311] 6.946006e-02 -4.173142e-01 1.072427e+00 1.072770e+00 -1.320920e+00
## [2316] -1.255928e-01 -7.910482e-01 5.809864e-01 -5.215394e-01 9.875277e-01
## [2321] -3.606605e-01 -1.067915e-01 1.340155e-01 1.019426e-01 -3.778954e-01
## [2326] 1.511499e-01 -1.280931e+00 5.418117e-03 -5.199328e-01 7.259552e-01
## [2331] -4.121534e-01 -3.381416e-01 -3.721462e-01 1.645707e-02 -1.813318e-01
## [2336] -1.457132e-01 3.965103e-01 1.271153e+00 -1.229254e+00 5.944972e-01
## [2341] -3.033579e-01 8.986426e-01 -3.606774e-01 6.675807e-01 8.097838e-02
## [2346] 3.897528e-02 1.404861e-01 -3.835540e-01 4.826128e-03 1.715989e+00
## [2351] -1.283629e+00 2.909751e-01 -1.354203e+00 1.367587e+00 -9.676718e-01
## [2356] -4.342063e-02 2.092971e-01 -8.298786e-01 4.071246e-01 -8.329789e-01
## [2361] -3.550915e-01 1.033805e+00 -7.422441e-01 9.061622e-01 -1.129881e+00
## [2366] 1.183751e+00 -1.145413e+00 4.999897e-01 1.571884e+00 -1.855743e+00
## [2371] 1.583831e+00 -5.479236e-02 8.082013e-01 1.426949e+00 -2.477432e+00
## [2376] -1.468830e+00 3.043687e+00 1.350129e+00 -1.130046e+00 6.993417e-01
## [2381] 5.206142e-01 -1.233383e+00 1.265370e+00 -1.052636e+00 5.744714e-01
## [2386] 1.047635e+00 -1.568990e+00 7.587609e-01 -8.535219e-01 1.077719e+00
## [2391] -1.108854e+00 4.712057e-02 1.213539e+00 -2.033657e+00 3.444650e-01
## [2396] -7.014986e-01 -2.756267e-01 6.561145e-01 -9.807971e-01 -4.850079e-01
## [2401] -1.406248e+00 1.058646e+00 -1.004552e+00 -8.530053e-01 1.901572e+00
## [2406] -1.534648e+00 1.017136e+00 -3.837381e-01 3.714795e-01 1.606990e+00
## [2411] -1.155507e+00 7.333540e-01 -1.196369e+00 1.211390e+00 -1.088384e+00
## [2416] 6.979370e-01 8.415188e-01 -1.974474e+00 7.876434e-01 -5.460637e-01
## [2421] -4.787844e-01 1.704754e+00 -6.018930e-01 1.147410e+00 -7.915748e-01
## [2426] 1.667570e+00 -1.034544e+00 3.880637e-01 -2.413720e-02 -1.117736e+00
## [2431] 1.087497e+00 -8.564089e-01 -2.530383e-01 -4.854223e-01 -1.864235e+00
## [2436] 1.339248e+00 -1.453492e+00 1.345171e+00 -8.539685e-01 5.351410e-02
## [2441] 2.299329e+00 -1.619539e+00 1.745334e+00 -2.948919e-01 4.387598e-01
## [2446] 1.412941e+00 -9.370984e-01 5.567436e-01 -1.207955e+00 1.285104e+00
## [2451] -1.071788e+00 4.641432e-01 1.574378e+00 -2.299621e+00 1.414891e+00
## [2456] -5.553872e-01 7.943689e-01 1.021359e+00 -1.081390e+00 1.037652e+00
## [2461] -1.324435e+00 1.358848e+00 -1.207537e+00 -4.515580e-01 7.894101e-01
## [2466] -8.656554e-01 1.521547e+00 1.708538e-01 -8.050074e-01 1.544292e+00
## [2471] -8.172728e-01 1.370015e+00 -1.250662e+00 8.615023e-01 -7.829683e-01
## [2476] 1.559023e-01 5.588374e-02 -4.017343e-01 5.129943e-01 -3.434943e-01
## [2481] -6.615427e-02 5.865769e-01 -1.209551e+00 8.049456e-01 -1.159729e+00
## [2486] 7.707706e-01 -7.440247e-01 5.003144e-01 9.550576e-01 -6.255674e-01
## [2491] 1.386672e+00 -1.699797e-01 2.609051e-01 1.530057e+00 -1.051703e+00
## [2496] -2.050080e+00 8.181372e-01 8.814344e-01 -7.852476e-01 5.255408e-01
## [2501] -3.853885e-01 -6.589775e-01 3.507101e-02 -3.428841e-01 6.618675e-02
## [2506] -2.324819e-01 -1.171174e+00 7.692464e-01 -1.011990e+00 9.439471e-01
## [2511] -7.919575e-01 1.272313e+00 2.172110e-01 -6.283946e-01 1.030875e+00
## [2516] -3.022415e-01 -2.072833e-01 7.306022e-01 -9.744004e-01 3.789622e-01
## [2521] -9.273360e-01 1.038601e+00 -5.352755e-01 -1.441114e-01 -7.198600e-01
## [2526] -5.067254e-01 2.496939e-01 -2.675395e-01 1.586368e-01 1.054609e+00
## [2531] -1.143660e+00 2.405314e-01 -7.862827e-01 1.060180e+00 -6.394000e-01
## [2536] -4.486087e-01 7.438833e-01 -4.585518e-01 9.466116e-01 -1.727179e-01
## [2541] 8.343240e-01 1.557085e-01 -6.496437e-01 1.095179e+00 -9.425916e-01
## [2546] 1.108234e+00 -6.989418e-01 -3.753751e-01 9.163571e-01 -4.246590e-01
## [2551] 1.344203e+00 -2.848829e-01 -4.025502e-01 1.174185e+00 -1.184332e+00
## [2556] 2.521035e-01 -8.729521e-01 1.080744e+00 -7.187097e-01 1.168962e-02
## [2561] -1.774554e-01 -4.352351e-01 1.045148e+00 -2.533503e-01 5.004982e-01
## [2566] 2.670145e-01 -1.154498e+00 1.319504e+00 -8.704483e-01 1.142759e+00
## [2571] -7.014125e-01 3.507332e-01 4.525860e-01 -4.381342e-01 2.797813e-01
## [2576] -2.632295e-01 4.063843e-01 2.589247e-01 -1.193328e+00 7.566380e-01
## [2581] -8.389533e-01 1.174888e+00 -7.456757e-01 -9.834505e-01 -1.104231e+00
## [2586] -5.014975e-01 2.402441e-01 -2.726659e-01 -1.498648e-01 9.356736e-01
## [2591] -7.069424e-01 6.435042e-01 -1.075551e+00 9.034283e-01 -7.356183e-01
## [2596] 2.812920e-01 -7.476284e-01 -4.554542e-01 9.844357e-01 9.695949e-03
## [2601] 8.816491e-01 3.029539e-01 -2.020069e+00 1.373226e+00 -9.087783e-01
## [2606] 6.557794e-01 -7.130780e-01 4.882079e-01 6.042546e-01 -5.550056e-01
## [2611] 1.007557e+00 -9.851202e-02 6.968709e-01 1.389753e+00 -1.438465e+00
## [2616] -3.092122e+00 1.383134e+00 2.068994e+00 -1.006365e+00 5.368137e-01
## [2621] -4.575124e-01 -1.290162e+00 -3.440932e-01 6.402278e-02 4.846423e-02
## [2626] 8.420781e-01 -1.356618e+00 -3.722108e-01 -8.569563e-01 8.049338e-01
## [2631] -5.925135e-01 1.212591e+00 6.188059e-01 -6.253988e-01 4.656676e-01
## [2636] -8.861228e-01 8.703797e-01 4.563222e-01 -6.608361e-01 -4.299350e-01
## [2641] -8.985945e-01 1.027335e+00 -1.362301e+00 -2.851381e-01 -5.926540e-01
## [2646] -2.885159e-01 8.088182e-02 3.419153e-04 2.032165e-01 8.432454e-01
## [2651] -1.412956e+00 1.123113e+00 -9.093186e-01 1.520617e+00 -1.138524e+00
## [2656] 7.759225e-01 -8.361176e-01 -4.998677e-01 1.524397e+00 1.128076e-02
## [2661] 2.669639e-01 1.152099e+00 -1.166993e+00 1.228581e+00 -8.600277e-01
## [2666] 1.009567e+00 -8.941642e-01 1.468115e+00 4.838091e-01 -9.974213e-01
## [2671] 1.566597e+00 -8.398922e-01 -3.852956e-01 6.189685e-01 -1.628883e+00
## [2676] 3.801099e-01 -1.143498e+00 6.924197e-01 -1.242258e+00 9.714048e-01
## [2681] 1.590451e+00 -4.628004e-01 1.111821e+00 1.523434e-01 5.204178e-01
## [2686] 6.379796e-01 -1.725236e+00 9.044203e-01 -1.384314e+00 5.766409e-01
## [2691] -1.270203e+00 6.127905e-01 9.077024e-01 -8.153728e-01 1.917493e-01
## [2696] 8.044710e-02 9.877069e-01 1.834904e+00 -1.948195e+00 6.287575e-01
## [2701] -1.347311e+00 1.102313e+00 -1.220304e+00 2.034508e-01 4.857536e-01
## [2706] -9.821428e-01 3.491508e-01 -9.914255e-02 -1.140603e+00 2.605640e+00
## [2711] -3.593624e-01 3.767476e-01 -1.351330e+00 1.175881e+00 -1.099743e+00
## [2716] 3.976677e-01 -1.891620e-02 -1.124704e+00 4.527619e-01 -5.632578e-01
## [2721] -1.133708e-01 6.574694e-01 -1.145734e+00 6.058182e-01 -1.322922e+00
## [2726] 1.280433e+00 -9.421618e-01 5.842069e-01 1.738465e+00 -1.427478e+00
## [2731] 9.162595e-01 -3.938521e-01 4.341944e-01 9.131320e-01 -1.737126e+00
## [2736] -2.304851e+00 3.065305e+00 9.013209e-01 -1.014472e+00 7.236612e-01
## [2741] 9.474241e-01 -1.301347e+00 6.031990e-01 -8.054219e-01 4.637459e-01
## [2746] 9.233683e-01 -8.499852e-01 1.061805e+00 -1.040475e+00 1.429138e+00
## [2751] -7.463142e-01 5.251611e-01 1.889599e-01 -1.484086e+00 9.352626e-01
## [2756] -6.235074e-01 3.946779e-01 5.417404e-01 -1.142577e+00 5.447312e-01
## [2761] -1.187416e+00 1.250540e+00 -1.130845e+00 1.660980e-01 2.023194e+00
## [2766] -1.378224e+00 5.538074e-01 -3.277950e-01 4.242861e-02 1.675366e-01
## [2771] -8.442370e-01 1.122793e-01 -1.056393e+00 1.173580e+00 -1.071597e+00
## [2776] -7.137760e-01 5.389609e-01 -1.628031e+00 1.676394e+00 -7.211042e-01
## [2781] 1.487998e+00 8.392492e-02 -3.261368e-01 1.192681e+00 -1.044430e+00
## [2786] 1.325943e+00 -1.246801e+00 4.487671e-01 9.816235e-01 -1.470308e+00
## [2791] 8.144025e-01 -7.398151e-01 7.607297e-01 1.025809e+00 -1.191271e+00
## [2796] 2.462204e-01 -1.163637e+00 1.586500e+00 -9.164818e-01 6.334041e-02
## [2801] 1.308390e+00 -1.485387e+00 6.990896e-01 -6.820685e-01 3.879082e-01
## [2806] -4.670604e-01 -1.570856e+00 1.587365e+00 -1.158275e+00 1.311085e+00
## [2811] -1.049101e+00 9.190650e-01 1.390241e+00 -1.393742e+00 1.713391e+00
## [2816] -9.237309e-01 4.765031e-01 3.775590e-01 -1.636264e+00 8.911938e-01
## [2821] -1.051117e+00 1.423548e+00 -1.046015e+00 5.834469e-01 1.633117e-01
## [2826] -1.494271e+00 1.323344e+00 -3.397217e-01 -2.931336e-01 6.395968e-01
## [2831] -4.606212e-01 3.587122e-01 -7.472484e-01 1.881392e-01 -3.732281e-01
## [2836] 1.885421e-01 -9.813313e-02 9.166144e-02 6.660063e-02 1.967180e-01
## [2841] 3.443420e-01 7.355500e-01 -5.937318e-01 5.775619e-01 -5.733066e-01
## [2846] 2.530523e-01 -1.401729e-01 -2.020114e-02 -9.977352e-02 1.249808e-01
## [2851] 2.072296e-02 -1.547251e-01 2.476458e-01 9.670518e-01 -5.173279e-01
## [2856] -1.148685e+00 6.748700e-01 4.143859e-01 -2.760303e-01 3.572834e-01
## [2861] 6.603618e-02 -9.491181e-02 -1.453153e-01 1.683245e-01 1.977070e-01
## [2866] 6.865045e-02 -7.496913e-01 1.551248e-01 -6.217678e-01 2.752451e-01
## [2871] -2.043387e-01 8.322220e-01 2.040409e-02 -6.266445e-02 -1.817001e-01
## [2876] -2.077053e-01 1.552846e-01 4.654378e-01 -5.233549e-01 -1.900510e-01
## [2881] -5.859464e-01 3.637076e-01 -4.094804e-01 2.685137e-02 2.004842e-02
## [2886] 3.477667e-02 -6.575380e-02 -1.257620e-01 9.030594e-02 -1.036320e-01
## [2891] -5.463623e-01 7.148635e-01 -5.365667e-01 4.376728e-01 -1.574384e-01
## [2896] -1.405335e-01 -1.122109e-01 9.034831e-02 2.293068e-01 -1.993854e-01
## [2901] -2.717405e-01 -1.301721e-01 -7.247971e-01 3.906287e-01 -5.842489e-01
## [2906] 3.803743e-01 -3.881081e-01 3.448049e-01 3.828174e-01 1.427611e-01
## [2911] 1.056598e-01 -3.233601e-01 7.470034e-01 7.292234e-01 -7.780940e-01
## [2916] 1.232457e-01 -4.908696e-01 2.569833e-01 -2.959375e-01 7.476338e-01
## [2921] -7.276070e-02 2.500557e-02 -3.649330e-02 -1.782120e-02 -2.563965e-01
## [2926] 4.204679e-01 -6.988629e-01 2.032489e-01 -4.318688e-01 4.241872e-01
## [2931] -2.836032e-01 -3.506586e-02 -6.636700e-02 2.032550e-01 -2.464551e-02
## [2936] -6.796344e-02 1.967661e-01 7.500456e-01 -6.978339e-01 6.619021e-01
## [2941] -2.268645e-01 5.781833e-01 -1.047165e-01 2.685356e-01 1.809524e-01
## [2946] 1.102071e-01 1.133498e-01 -1.681555e-01 -2.248250e-01 1.143254e+00
## [2951] -3.991187e-01 5.326333e-01 -3.681300e-02 3.570718e-01 4.974895e-01
## [2956] 2.146520e-01 -1.270551e-01 3.796633e-02 1.116263e-01 -3.691123e-01
## [2961] 6.060296e-01 4.364563e-02 3.265070e-01 -2.489526e-01 1.787649e-01
## [2966] -6.597514e-02 5.269101e-02 -5.582926e-02 -4.340413e-01 -5.527287e-01
## [2971] 9.818723e-02 6.946253e-01 8.253391e-01 1.597970e-01 -1.443686e-01
## [2976] -9.992807e-03 -2.352369e-01 -3.973217e-01 3.550130e-03 5.961329e-02
## [2981] -7.794566e-01 -6.817508e-01 1.427703e-01 -1.090814e-01 6.464317e-03
## [2986] -4.372358e-01 -5.345867e-01 9.746951e-01 -4.332596e-01 7.181068e-01
## [2991] -5.130372e-02 -1.132631e-01 -4.848296e-02 -2.388202e-01 -3.417455e-02
## [2996] -4.924083e-01 7.487469e-01 -4.353518e-01 9.125878e-01 3.668044e-01
## [3001] -4.805001e-02 -7.651770e-04 -2.755394e-01 7.413601e-01 -4.888978e-01
## [3006] 9.747377e-01 -4.718376e-01 1.152105e+00 3.939585e-01 -1.254261e-01
## [3011] -3.679892e-03 -1.672760e-01 -1.079436e-02 -5.113226e-01 1.156279e+00
## [3016] -3.578809e-01 9.346614e-01 -2.935654e-01 -9.654330e-02 -9.710039e-02
## [3021] -1.881679e-01 3.840480e-01 -4.871324e-01 -2.014645e-01 -3.292104e-01
## [3026] -1.039924e-01 -5.596214e-01 -1.181909e-01 2.399433e-02 -1.241376e-01
## [3031] -4.095647e-01 -4.800845e-01 2.682186e-02 -3.159058e-01 -6.205394e-01
## [3036] -8.237254e-01 -1.662234e-01 -2.901639e-02 -3.944276e-03 8.064584e-01
## [3041] -4.757151e-01 1.007704e+00 -1.512460e-01 7.553524e-01 -4.752061e-01
## [3046] -9.687628e-02 3.331393e-02 -7.721659e-02 1.415932e-01 -4.584731e-01
## [3051] 3.198882e-01 -1.238802e-01 8.835850e-03 -2.372855e-01 -1.599451e-01
## [3056] 7.625343e-02 -3.787281e-03 1.217468e+00 -7.193463e-01 -2.610182e-01
## [3061] -3.246942e-01 4.185989e-01 -3.179162e-01 -2.994995e-01 -3.702534e-01
## [3066] 1.409110e-01 -8.682908e-02 -7.982746e-02 7.086636e-01 -1.296155e-02
## [3071] -8.756072e-01 5.766692e-01 -3.250956e-01 3.774978e-01 -3.903145e-01
## [3076] -1.521071e-01 -4.466382e-01 -2.181417e-02 -1.314999e-01 -8.013342e-02
## [3081] -1.385667e-02 1.029952e+00 -8.164468e-01 9.206217e-01 -3.408803e-01
## [3086] 6.019537e-01 -3.325000e-01 -6.042937e-02 -4.906935e-01 1.356470e-02
## [3091] 8.555543e-02 -1.126336e-01 -9.480108e-02 1.381639e+00 -8.043767e-01
## [3096] 2.419886e-01 -3.450323e-01 4.681588e-01 -2.990554e-01 2.985405e-01
## [3101] -3.069926e-01 3.226087e-02 1.645114e-01 -7.777989e-02 2.778060e-01
## [3106] 6.263011e-01 -1.067384e+00 3.812810e-01 -6.433507e-01 3.491277e-01
## [3111] -5.023139e-01 7.273257e-01 -4.404871e-01 -2.476935e-01 -2.338817e-01
## [3116] -2.788105e-01 4.116560e-01 4.407732e-01 -8.239000e-01 6.892519e-01
## [3121] -6.337946e-01 2.816764e-01 -5.447321e-01 2.030921e-01 4.070943e-01
## [3126] -1.182361e-01 3.761779e-01 -1.736734e-01 9.239846e-01 1.412771e-01
## [3131] -7.028060e-01 4.551293e-01 -6.344586e-01 4.056269e-01 -5.294957e-01
## [3136] -2.354037e-01 2.399034e-01 -9.360923e-02 5.333912e-01 -1.736547e-02
## [3141] -2.372125e-01 2.377157e-01 -1.052608e+00 1.220929e+00 -3.031154e-01
## [3146] 3.480226e-01 -4.469934e-01 1.041715e+00 -6.428040e-02 -3.427545e-01
## [3151] 9.359899e-02 -3.224103e-01 -2.041899e-02 4.847414e-01 -1.007716e+00
## [3156] 1.131270e+00 -3.469574e-01 2.823244e-01 -5.610889e-01 5.709077e-01
## [3161] 1.968770e-02 -2.759245e-01 4.847375e-01 -5.240922e-02 -5.758261e-02
## [3166] -2.560240e-01 -8.779988e-01 8.528866e-01 -6.641564e-01 4.007798e-01
## [3171] -4.039889e-01 -2.053478e-01 -3.045214e-01 -1.788174e-01 -2.092619e-02
## [3176] -1.167649e-01 -2.682974e-01 1.621071e-01 -1.017293e+00 1.361760e+00
## [3181] -3.867327e-01 3.328816e-01 -6.854738e-01 1.999585e-01 -6.206535e-01
## [3186] -3.434985e-01 -1.362821e-01 -8.915232e-02 -5.573744e-03 9.323318e-01
## [3191] -9.220977e-01 5.199501e-01 -6.730669e-01 3.543009e-01 -4.347448e-01
## [3196] 1.264544e+00 2.588306e-01 -2.157892e-01 5.898850e-02 -4.617844e-02
## [3201] 5.941984e-01 5.083691e-01 -1.327424e+00 5.005072e-01 -1.916460e+00
## [3206] 1.623907e+00 -1.761326e+00 -3.261776e-01 6.535822e-01 -1.497300e+00
## [3211] -3.357352e-02 -4.445948e-02 4.942770e-01 1.406834e-01 -2.677189e+00
## [3216] 3.738616e+00 -1.323243e+00 1.559302e+00 -1.777561e+00 5.265664e-01
## [3221] -6.427640e-02 -1.888942e+00 1.098809e+00 -3.042310e-01 5.881189e-01
## [3226] 2.570570e+00 -1.737134e+00 2.221757e+00 -2.101711e+00 1.755516e+00
## [3231] -1.552619e+00 7.351257e-01 2.467050e-01 -1.596739e+00 7.729895e-01
## [3236] -1.465088e+00 -5.414797e-01 1.869604e+00 -3.259849e+00 1.035068e+00
## [3241] -2.305695e+00 1.304783e+00 -2.177164e+00 2.295520e-01 -3.229907e-01
## [3246] -2.300118e+00 1.181802e+00 -1.552597e+00 -1.247285e-01 2.245232e+00
## [3251] -2.221735e+00 1.997816e+00 -1.654403e+00 1.560916e+00 -1.932195e+00
## [3256] 3.250330e+00 6.640295e-01 -1.909284e+00 3.538350e-01 -5.374898e-01
## [3261] 9.732187e-01 7.309304e-01 -1.482730e+00 2.569474e+00 -1.619378e+00
## [3266] 1.454322e+00 -1.553087e+00 1.923823e+00 1.561374e+00 -1.707843e+00
## [3271] 3.163561e+00 -3.733138e-02 1.459052e+00 6.924211e-01 -1.000705e+00
## [3276] 1.875549e+00 -1.430954e+00 1.986170e+00 -1.808003e+00 1.611213e+00
## [3281] 1.891737e+00 -1.149263e+00 1.994860e+00 -5.788302e-01 -9.439020e-01
## [3286] 8.762803e-01 -2.847852e+00 3.085957e+00 -1.274642e+00 1.584576e+00
## [3291] -1.858763e+00 1.814424e+00 2.149309e+00 -2.154080e+00 2.150918e+00
## [3296] -1.453884e+00 7.611907e-02 8.223929e-01 -2.814024e+00 1.084004e+00
## [3301] -1.977983e+00 1.369340e+00 -1.681680e+00 1.266097e+00 2.372399e+00
## [3306] -2.508648e+00 3.361382e+00 -1.259253e+00 2.547477e-01 -9.301865e-01
## [3311] -1.669895e+00 1.110135e+00 -1.649530e+00 1.387724e+00 -2.089698e+00
## [3316] -9.473187e-01 1.752461e-01 -2.453695e+00 1.414939e+00 -4.652767e-01
## [3321] 4.546751e-01 1.787134e-01 -2.615234e+00 3.676796e+00 -1.779686e+00
## [3326] 1.365842e+00 -1.804596e+00 9.131785e-01 7.331694e-01 -2.532202e+00
## [3331] 1.391425e+00 -1.119914e+00 -1.693557e-01 1.079733e+00 -1.422254e+00
## [3336] 9.078939e-01 -1.894557e+00 1.529146e+00 -1.884266e+00 1.101486e+00
## [3341] 2.386955e+00 -2.076329e+00 9.012143e-01 9.129877e-03 1.329908e+00
## [3346] 8.421876e-01 -9.379187e-01 3.578135e-01 -9.624717e-01 1.750054e+00
## [3351] -1.047865e+00 -3.248646e-01 -1.086765e+00 -1.643191e-01 1.117667e+00
## [3356] -3.326525e-01 9.308826e-01 -1.152184e+00 -8.020532e-01 -5.406350e-02
## [3361] -1.162705e+00 1.544922e+00 -1.105346e+00 -3.403642e-01 -3.403336e-01
## [3366] -1.579639e+00 -2.732701e-01 2.051597e-01 4.926917e-01 -5.948498e-01
## [3371] -1.085227e+00 3.567651e-02 -1.461632e+00 1.502316e+00 -1.230185e+00
## [3376] -4.204994e-01 -4.415041e-02 -1.517611e+00 2.234627e-01 -1.043433e+00
## [3381] -6.512566e-01 3.131421e-01 -2.502428e+00 -9.822350e-02 -1.682710e+00
## [3386] 7.176355e-01 -1.679652e+00 -3.212310e-01 -1.191444e+00 -1.959617e+00
## [3391] 6.651221e-01 -1.009674e+00 -6.276602e-02 8.617018e-02 -1.464725e+00
## [3396] 2.109558e+00 -6.218004e-01 1.249663e+00 -1.210757e+00 2.034565e+00
## [3401] 2.744662e+00 -1.876121e+00 1.960878e+00 -1.143686e+00 -1.731894e-02
## [3406] 1.128727e+00 -1.151335e+00 1.619009e+00 -1.319107e+00 1.010451e+00
## [3411] -1.064459e+00 2.631503e+00 1.793071e+00 -2.058301e+00 2.346667e+00
## [3416] 2.038541e-01 6.784755e-01 1.037916e+00 -9.769913e-01 2.199718e+00
## [3421] -1.770353e+00 1.041013e+00 -2.019536e+00 2.392410e+00 3.118664e+00
## [3426] -1.682801e+00 3.158601e+00 7.820086e-01 8.075680e-01 1.874417e+00
## [3431] -1.180794e+00 1.430189e+00 -1.743297e+00 6.318376e-01 -1.862699e+00
## [3436] 1.674237e+00 9.683908e-01 -1.552826e+00 7.381908e-01 -1.499377e+00
## [3441] 7.334106e-01 1.861204e+00 -2.978447e+00 1.475647e+00 -1.235052e+00
## [3446] 7.082222e-01 -1.950824e+00 1.937266e+00 7.184943e-01 -1.920957e+00
## [3451] 2.420086e+00 -1.642819e+00 -1.002693e+00 8.746574e-01 -1.674850e+00
## [3456] 3.868849e+00 -1.675985e+00 3.114839e-01 -1.709152e+00 7.691533e-01
## [3461] 8.953519e-01 -2.834560e+00 4.460142e-01 -1.500396e+00 6.664013e-01
## [3466] -2.888404e-01 3.654667e-01 1.854796e+00 -1.654665e+00 7.969244e-01
## [3471] -1.976381e+00 1.743241e+00 3.554877e+00 -2.489643e+00 1.916850e+00
## [3476] -6.816683e-01 5.064365e-02 5.301592e-01 -1.169838e+00 6.700912e-01
## [3481] -2.156309e+00 9.359624e-01 -1.413312e+00 -3.664390e-01 4.755096e-01
## [3486] -1.237993e+00 1.303071e+00 -6.230628e-01 -3.836624e-01 4.879435e-01
## [3491] -1.152375e+00 1.332072e+00 -1.014512e+00 8.455024e-01 -7.175193e-01
## [3496] -1.403306e-01 8.234761e-01 -4.750335e-01 1.947605e+00 1.110003e-01
## [3501] 1.420191e-01 -3.360589e-01 -1.770264e+00 -6.281610e-01 -1.158778e+00
## [3506] 8.743579e-01 -8.180519e-01 -8.301481e-01 -1.959681e-01 -1.006722e+00
## [3511] -9.367635e-02 -5.983333e-01 -7.064253e-01 1.805604e+00 -1.727227e+00
## [3516] -3.515352e-01 -1.520148e+00 8.742389e-01 -1.391966e+00 3.441964e-01
## [3521] 6.786122e-01 -1.047246e+00 1.372372e+00 7.473352e-03 -9.031574e-02
## [3526] 4.675966e-01 -2.131339e+00 -3.882400e-01 -1.598887e+00 5.821984e-01
## [3531] -1.285522e+00 -2.643707e-01 -2.282731e-01 -1.691109e+00 1.730396e-01
## [3536] -3.456161e-01 -3.974485e-01 -5.818024e-01 -1.878394e+00 2.214283e+00
## [3541] -8.905141e-01 1.225763e+00 -9.435241e-02 1.628011e+00 1.963946e+00
## [3546] -1.017836e+00 7.573625e-01 -7.045732e-01 1.248800e+00 3.275762e+00
## [3551] -2.310047e+00 2.190205e+00 -5.052513e-01 1.049870e+00 -6.110231e-01
## [3556] 8.064850e-01 1.085750e+00 -1.214157e+00 5.729072e-01 -5.314686e-01
## [3561] 8.181751e-01 3.154057e+00 -1.313089e+00 2.397747e+00 -1.527921e+00
## [3566] 1.116984e+00 -9.305278e-01 2.642811e-01 1.064624e-01 -1.074265e+00
## [3571] 1.403935e+00 -6.619865e-01 8.626912e-01 1.601254e+00 -2.612712e+00
## [3576] 1.724084e+00 -1.122972e+00 8.027311e-01 -1.080802e+00 2.571876e+00
## [3581] 1.328248e+00 -1.459851e+00 5.127563e-01 5.650770e-01 9.287103e-01
## [3586] 6.886963e-01 -2.250295e+00 1.927626e+00 -1.189017e+00 1.030944e+00
## [3591] -1.400137e+00 2.124866e+00 7.810161e-01 -1.865512e+00 8.992801e-01
## [3596] -6.156602e-01 -5.539593e-01 2.052180e+00 -2.560156e+00 1.568844e+00
## [3601] -9.251786e-01 1.169627e+00 -1.450314e+00 1.268012e+00 -2.294172e-01
## [3606] -1.769822e+00 -4.208407e-01 -5.979331e-01 9.614197e-01 7.576433e-01
## [3611] -2.232437e+00 1.903178e+00 -1.722530e+00 1.008724e+00 -1.377572e+00
## [3616] 5.226471e-01 8.129174e-01 -1.438319e+00 9.768863e-01 -5.119399e-01
## [3621] 5.743134e-02 1.327176e+00 -2.510935e+00 2.110698e+00 -1.043897e+00
## [3626] 8.662328e-01 -1.357882e+00 -9.768945e-02 1.117469e+00 -1.708532e+00
## [3631] 1.576913e+00 -7.584870e-02 3.007056e-01 -7.164447e-01 -1.363971e+00
## [3636] 5.846780e-01 -1.622945e+00 4.252661e-01 -1.270363e+00 6.747819e-01
## [3641] -1.619818e-01 -5.402969e-01 1.129968e+00 4.722755e-02 1.341828e-01
## [3646] -3.416428e-01 -1.550234e+00 -4.508945e-01 -8.449438e-01 3.425630e-01
## [3651] -1.463046e+00 -4.287725e-01 -1.543850e-01 -1.006204e+00 -2.767412e-01
## [3656] 1.126920e-01 -4.652458e-01 1.064249e+00 -1.387540e+00 5.495660e-01
## [3661] -9.262545e-01 5.478403e-01 -9.428409e-01 1.138490e+00 1.041002e-01
## [3666] -6.374899e-01 1.218351e+00 2.800847e-01 9.688343e-02 6.383222e-01
## [3671] -1.160749e+00 1.378587e+00 -1.981767e+00 2.063091e-01 -8.478103e-01
## [3676] -4.625312e-01 -2.042404e-01 -1.523595e+00 7.442682e-01 -6.882787e-01
## [3681] 4.290820e-01 -4.345564e-01 -2.329677e+00 1.368687e+00 -3.313687e-01
## [3686] 1.413100e+00 -7.193049e-01 1.516645e+00 1.324417e+00 -2.915575e-01
## [3691] 6.294370e-01 -5.395097e-01 -3.660606e-02 1.853067e+00 -2.056840e+00
## [3696] 2.589061e+00 -4.996716e-01 8.878038e-01 -7.016073e-02 2.952570e-01
## [3701] -2.612788e-01 -1.149779e+00 1.598138e+00 -6.004845e-01 1.416961e+00
## [3706] 2.283733e+00 -2.952089e-01 3.438116e-03 -7.248624e-01 9.561906e-01
## [3711] 1.130925e-01 6.641721e-01 4.977986e-01 -9.943686e-01 -1.981758e-01
## [3716] -4.134874e-01 5.968003e-01 1.258196e+00 -2.511518e+00 1.378921e+00
## [3721] -7.307412e-01 9.512595e-01 -6.010729e-01 5.127020e-01 4.757794e-01
## [3726] -7.676188e-01 2.865101e-01 6.909190e-01 1.659493e+00 9.651208e-01
## [3731] -2.071724e+00 1.192468e+00 6.188097e-05 8.341512e-02 -6.538920e-01
## [3736] 2.080401e+00 3.649371e-01 -1.996906e+00 1.771152e+00 -4.636727e-01
## [3741] -6.530977e-01 1.309637e+00 -2.848226e+00 1.575465e+00 -7.268701e-01
## [3746] 1.818986e+00 -8.283251e-01 1.117905e+00 3.127481e-01 -6.294541e-01
## [3751] -8.058584e-01 -7.738793e-01 5.201169e-01 9.237874e-01 -1.387465e+00
## [3756] 1.503431e+00 -1.435550e+00 5.934187e-01 -1.334601e+00 -1.914294e-01
## [3761] 1.002569e+00 -1.561124e+00 5.611503e-01 -2.697413e-01 -6.207227e-02
## [3766] 1.193956e+00 -1.334884e+00 1.352849e+00 1.349052e-01 5.783253e-01
## [3771] -1.064072e+00 -1.462825e+00 1.022973e-01 -7.037192e-01 2.278858e-01
## [3776] 5.285516e-01 -1.044789e-01 2.214277e-01 -1.124919e-01 -1.174724e-01
## [3781] -1.513858e+00 1.286426e+00 -1.398626e+00 5.644233e-01 9.168058e-02
## [3786] -8.702820e-01 2.297036e+00 -1.083568e-01 8.159513e-01 -1.193215e+00
## [3791] -1.251990e+00 5.076075e-01 -1.096823e+00 1.266625e+00 -1.515188e+00
## [3796] 1.230930e+00 6.181396e-01 -1.961301e+00 9.971442e-02 -5.941659e-02
## [3801] 2.790252e-01 -5.474340e-02 -7.602924e-01 4.003669e-01 -1.616986e+00
## [3806] 1.164025e+00 -1.656200e+00 1.160881e+00 5.964394e-01 -1.412182e+00
## [3811] 1.245919e+00 -9.665004e-01 -7.653697e-01 8.444369e-01 -2.122394e+00
## [3816] 1.325731e+00 -1.790259e+00 8.594311e-01 -1.802093e+00 3.083958e-02
## [3821] 2.834040e-01 -2.343989e+00 1.446526e+00 -1.131596e+00 1.102105e-01
## [3826] 1.051977e+00 -2.565526e+00 1.208151e+00 -5.381517e-01 1.286816e+00
## [3831] -1.375431e+00 1.460539e+00 1.368068e+00 -2.164138e+00 9.014526e-01
## [3836] -7.824519e-01 -1.165259e-01 8.025469e-01 -1.352824e+00 6.393283e-01
## [3841] -1.338652e+00 1.379667e+00 -1.146107e+00 2.261673e+00 1.634394e+00
## [3846] -2.294064e+00 1.443237e+00 5.854815e-01 4.937706e-01 1.549415e+00
## [3851] 9.027044e-02 2.322070e+00 -1.223911e+00 1.282048e+00 -1.491758e+00
## [3856] 1.770447e+00 2.308127e+00 -1.802688e+00 2.320347e+00 5.471859e-01
## [3861] 6.291507e-01 1.735131e+00 -1.104610e+00 1.098615e+00 -9.988044e-01
## [3866] 1.009871e+00 -1.504692e+00 4.925658e-01 9.345626e-01 -2.134695e+00
## [3871] 7.315916e-01 -7.568735e-01 7.661635e-01 1.003047e+00 -2.184755e+00
## [3876] 9.123513e-01 -1.215003e+00 8.753248e-01 -1.629205e+00 1.068508e+00
## [3881] 3.009457e-01 -2.202347e+00 1.467258e+00 -7.432915e-01 -1.114050e+00
## [3886] 6.626146e-01 -2.580737e+00 2.690433e+00 -1.351579e+00 9.516520e-01
## [3891] -1.337263e+00 1.605339e+00 7.551426e-01 -2.566303e+00 1.217673e-01
## [3896] -4.559911e-01 1.053193e+00 4.223262e-01 -7.844194e-01 1.809112e-01
## [3901] -5.650319e-01 1.208505e+00 -1.647533e+00 2.204009e-02 2.574809e+00
## [3906] -2.265506e+00 1.928286e+00 2.899897e-01 -4.178525e-01 -3.260412e-02
## [3911] -6.733739e-01 2.027613e+00 -9.478963e-01 1.350060e+00 -1.326026e+00
## [3916] -1.915019e+00 7.822155e-01 -1.838669e+00 1.911664e+00 -1.660578e-01
## [3921] -3.536472e-01 3.802924e-01 -1.061908e+00 -3.994618e-02 -6.554700e-01
## [3926] 5.798760e-01 -5.059561e-01 6.041839e-02 -3.130599e-01 7.970951e-02
## [3931] 4.276326e-02 -1.094039e-01 6.574214e-01 3.075864e-02 -1.047169e+00
## [3936] 7.710520e-01 -6.162547e-01 6.230265e-01 -4.738225e-01 -4.990621e-01
## [3941] -5.149788e-01 -5.647527e-02 -1.005553e-02 -1.258032e-01 -1.474292e-01
## [3946] 1.318570e+00 -1.112607e+00 1.310339e+00 -6.582647e-01 6.253007e-01
## [3951] -4.588417e-01 -2.720693e-01 -6.837977e-01 -5.294849e-02 9.536910e-02
## [3956] -8.101062e-02 3.029021e-01 1.746418e+00 -9.872027e-01 2.493962e-01
## [3961] -4.695426e-01 6.639181e-01 -4.611221e-01 5.008809e-01 -3.307830e-01
## [3966] 3.939771e-02 1.674072e-01 -5.305080e-02 4.134785e-01 4.829343e-01
## [3971] -1.309555e+00 8.522809e-01 -8.634168e-01 5.116494e-01 -6.061138e-01
## [3976] 1.036015e+00 -3.336325e-01 -3.068411e-01 -1.266700e-01 -1.450177e-01
## [3981] 9.068748e-02 1.068605e+00 -1.181003e+00 1.417215e+00 -9.497988e-01
## [3986] 4.710941e-01 -7.402518e-01 4.895391e-01 4.872073e-01 -2.402850e-01
## [3991] 3.302987e-01 -2.025227e-01 7.933537e-01 1.624022e-01 -1.278901e+00
## [3996] 8.319931e-01 -8.489754e-01 4.617470e-01 -7.122543e-01 -4.164160e-01
## [4001] 1.619964e-01 -2.821127e-01 2.908825e-01 -2.504925e-01 -2.244698e-01
## [4006] 4.940392e-01 -1.268215e+00 1.632215e+00 -7.095939e-01 5.650157e-01
## [4011] -5.688674e-01 1.265353e+00 -2.204636e-01 -3.752913e-01 1.324192e-01
## [4016] -2.108553e-01 2.244956e-01 7.883490e-01 -1.260921e+00 1.548665e+00
## [4021] -7.292732e-01 4.984841e-01 -6.906622e-01 1.178109e+00 -1.157345e-01
## [4026] -2.588117e-01 4.236379e-01 -1.659576e-01 1.938865e-01 -2.404108e-01
## [4031] -1.151849e+00 7.645803e-01 -8.160657e-01 6.423196e-01 -6.021000e-01
## [4036] -2.436886e-01 -1.834453e-01 -1.804744e-01 1.382489e-01 8.445000e-03
## [4041] -1.735420e-01 -4.519123e-02 -1.218775e+00 1.484482e+00 -6.692555e-01
## [4046] 5.852852e-01 -6.985129e-01 2.675583e-02 -7.539581e-01 -3.044229e-01
## [4051] -1.806344e-02 1.639641e-02 1.306869e-01 1.348564e+00 -1.185372e+00
## [4056] 4.640870e-01 -7.028976e-01 6.273455e-01 -5.671930e-01 1.873864e+00
## [4061] 1.790425e-01 -2.715990e-01 1.342152e-01 -3.615828e-02 1.101098e-01
## [4066] 1.395105e-01 -7.091582e-01 -4.483778e-01 2.681890e-01 -9.456117e-01
## [4071] 3.447090e-01 -4.855902e-01 6.828779e-01 -2.607753e-01 -7.463470e-03
## [4076] 6.632253e-01 -7.065072e-01 5.464839e-01 2.433139e-01 -1.118058e+00
## [4081] -9.232728e-02 -5.320025e-01 6.687197e-01 -2.803345e-01 -1.212541e-02
## [4086] 4.183303e-01 -7.957037e-01 1.535958e-01 1.342913e-01 -5.556144e-01
## [4091] 5.720567e-01 -5.509060e-01 3.572221e-01 -2.150283e-01 4.731780e-01
## [4096] 8.126638e-01 -8.264977e-01 4.090902e-01 1.770352e-01 -6.904188e-01
## [4101] -3.036770e-01 -6.822562e-01 2.973816e-02 -1.484200e-01 -1.732336e-02
## [4106] 3.705785e-01 -1.140217e+00 1.268538e+00 -2.771649e-01 7.244701e-01
## [4111] 1.558937e+00 -1.100214e+00 5.419625e-01 -7.567471e-01 -5.334758e-01
## [4116] 8.865563e-01 -1.244450e+00 2.003413e-01 -4.052273e-01 6.556004e-01
## [4121] 1.543879e+00 -1.191213e+00 1.941251e+00 -7.879545e-01 -6.743167e-01
## [4126] 2.781591e-01 -1.341491e+00 7.024302e-01 -4.432287e-01 6.454175e-01
## [4131] 2.569999e-01 -1.314149e+00 7.567776e-01 -7.097116e-01 7.666146e-01
## [4136] 1.145078e+00 -1.324203e+00 1.002222e+00 -4.089031e-01 1.784568e+00
## [4141] 2.161670e+00 -1.241139e+00 9.357399e-01 -8.027947e-01 -3.474265e-01
## [4146] 1.099248e+00 -1.391045e+00 7.410799e-01 -3.188597e-01 4.670905e-01
## [4151] -1.472499e-01 -1.395396e+00 6.038550e-02 -8.886526e-01 -5.520363e-01
## [4156] 1.195405e+00 -1.398668e+00 -6.902690e-01 -4.856956e-01 8.511750e-01
## [4161] 1.812872e+00 -1.430972e+00 5.901807e-01 -4.356039e-01 2.033329e-01
## [4166] 1.459022e+00 -1.196975e+00 7.735268e-01 -3.631003e-01 -6.029720e-01
## [4171] 1.415870e+00 -1.311058e+00 1.429823e+00 -6.482488e-01 -1.601826e-01
## [4176] 5.127305e-01 -1.268400e+00 5.703614e-01 -4.119241e-01 1.631524e-01
## [4181] 1.616718e+00 -1.448882e+00 6.855885e-01 -8.474712e-01 -5.605158e-01
## [4186] 1.191850e+00 -6.087786e-01 -3.654955e-01 -2.505121e-01 4.382021e-01
## [4191] -3.143372e-01 1.051860e-01 -2.668227e-01 6.158190e-02 -1.296581e-01
## [4196] -7.201876e-02 6.039190e-01 -8.403240e-02 -8.092828e-01 2.781632e-01
## [4201] -4.191244e-01 3.267236e-01 -4.014068e-01 -3.473403e-01 -3.930685e-01
## [4206] -1.001579e-01 -4.406830e-02 -8.988247e-02 9.563102e-04 9.662573e-01
## [4211] -8.741427e-01 8.053402e-01 -3.497894e-01 5.014008e-01 -3.965551e-01
## [4216] -6.553483e-02 -4.543852e-01 -5.884846e-02 1.272095e-01 -1.594983e-01
## [4221] -1.893925e-01 1.546833e+00 -8.479563e-01 2.277058e-01 -4.457140e-01
## [4226] 3.215010e-01 -3.796352e-01 1.658986e-01 -2.838687e-01 -9.765500e-02
## [4231] 1.602412e-01 -7.269179e-02 3.231058e-01 1.111047e+00 -1.057921e+00
## [4236] 7.873465e-01 -4.911907e-01 3.998442e-01 -4.228638e-01 1.029389e+00
## [4241] -3.040975e-01 -2.879730e-01 -1.638267e-01 -2.734087e-01 3.979430e-01
## [4246] 7.460205e-01 -8.338611e-01 6.668430e-01 -4.928171e-01 9.645084e-02
## [4251] -6.102369e-01 3.792177e-01 3.688736e-01 -1.909427e-01 2.246229e-01
## [4256] -1.582683e-01 7.532829e-01 -2.050607e-01 -6.204559e-01 5.325401e-01
## [4261] -4.445240e-01 4.337491e-01 -2.273110e-01 -4.405277e-01 1.665128e-01
## [4266] -1.989928e-01 7.417608e-01 -1.085446e-01 -7.955088e-02 5.707064e-01
## [4271] -1.064047e+00 1.072561e+00 -2.167965e-01 3.614767e-01 -3.661390e-01
## [4276] 9.042388e-01 -1.325689e-01 -3.737397e-01 1.203925e-01 -2.774682e-01
## [4281] 3.715120e-02 1.794558e-01 -9.254802e-01 1.034398e+00 -3.038580e-01
## [4286] 2.253173e-01 -4.521126e-01 5.621331e-01 1.071885e-01 -2.707955e-01
## [4291] 6.575222e-01 -1.372101e-01 1.857477e-01 -3.071117e-01 -7.545697e-01
## [4296] 5.486933e-01 -5.786160e-01 3.378651e-01 -3.501376e-01 -3.864489e-01
## [4301] -4.242563e-01 -4.843319e-02 1.636292e-01 -1.263839e-01 -2.381073e-01
## [4306] 1.663226e-01 -9.605102e-01 1.283593e+00 -2.849705e-01 2.903113e-01
## [4311] -6.620819e-01 -6.148373e-02 -6.368590e-01 -3.560111e-01 -7.346543e-02
## [4316] -5.093698e-02 7.116032e-02 8.759471e-01 -7.784673e-01 4.792883e-01
## [4321] -5.874832e-01 3.529888e-01 -2.724368e-01 1.114130e+00 4.117552e-01
## [4326] -2.569137e-01 9.262583e-02 1.407648e-01 2.816415e-01 9.044384e-03
## [4331] -1.229947e+00 1.732311e-02 -1.427847e+00 2.597961e-01 -1.377073e+00
## [4336] 1.239143e+00 1.169461e-02 -1.523713e-01 2.188316e+00 -5.035883e-01
## [4341] -4.178018e-01 5.236987e-02 -1.105769e+00 -5.627347e-01 -4.839765e-01
## [4346] 5.786229e-01 -9.933679e-01 -8.760597e-02 -2.391732e-01 -5.518338e-01
## [4351] -6.821783e-01 4.124264e-01 -6.358304e-01 1.224940e+00 -1.485575e+00
## [4356] 6.179339e-01 -1.074309e+00 1.158676e+00 -7.343846e-01 1.195017e+00
## [4361] 1.223912e-01 -1.892686e-01 6.663342e-01 3.594289e-01 -1.343312e-01
## [4366] -4.122612e-02 -1.239814e+00 8.634824e-01 -2.375528e+00 6.173014e-01
## [4371] -1.103302e+00 -6.462276e-01 -5.516484e-01 -1.547709e+00 3.457550e-01
## [4376] -1.286466e+00 8.161748e-01 -3.267174e-01 -1.495602e+00 6.836133e-01
## [4381] 5.429795e-02 1.022954e+00 -7.921584e-01 1.665751e+00 1.055392e+00
## [4386] -9.496426e-01 1.150342e-01 -2.919863e-01 -6.273167e-01 2.189589e+00
## [4391] -2.683191e+00 1.896310e+00 7.913634e-03 6.678847e-01 -4.533025e-01
## [4396] 9.471299e-01 6.285875e-01 -1.929267e+00 1.283649e+00 1.569210e-01
## [4401] 1.278618e+00 1.994734e+00 -3.455470e-01 1.341248e+00 -1.023294e+00
## [4406] 1.720715e+00 -4.097592e-01 1.364033e+00 8.675685e-01 -1.659917e-01
## [4411] -1.210065e-01 -3.377754e-01 9.079714e-01 1.036433e+00 -1.452239e+00
## [4416] 1.691101e+00 -1.027847e+00 8.550892e-01 -8.195500e-01 1.616281e-01
## [4421] -6.904122e-02 -1.764003e+00 4.274547e-01 -9.294326e-02 2.264382e+00
## [4426] -2.658485e-01 -2.084360e+00 6.635734e-01 -8.208792e-01 6.388120e-01
## [4431] -1.222055e+00 1.239988e+00 1.092763e+00 -2.020628e+00 1.977560e+00
## [4436] -3.069448e-02 -1.214479e+00 1.165447e+00 -2.516315e+00 2.005750e+00
## [4441] -1.024686e+00 1.591398e+00 -2.683776e-01 1.633389e+00 -6.495726e-01
## [4446] -8.388081e-01 -5.642058e-01 -2.302525e-01 1.274693e-01 1.350170e+00
## [4451] -1.627541e+00 8.478375e-01 -1.118240e+00 1.178781e+00 -1.098887e+00
## [4456] -5.574178e-02 4.604183e-02 -7.811421e-01 1.045343e+00 -4.207865e-01
## [4461] 2.118620e-03 3.189423e-01 -1.511590e+00 6.360641e-01 -4.302820e-01
## [4466] 5.510870e-01 -7.907280e-01 -1.233317e+00 1.552757e+00 -2.066594e-01
## [4471] 1.120208e-01 1.316270e-01 3.621887e-01 2.778437e-01 -1.009783e+00
## [4476] 2.263129e-03 -5.025575e-01 6.549012e-01 -3.878377e-01 -3.086230e-01
## [4481] -4.021849e-01 1.332163e-01 -6.447893e-02 -5.468810e-02 7.398849e-01
## [4486] -2.155447e-02 -1.202512e+00 1.084143e+00 -4.291737e-01 5.884447e-01
## [4491] -4.784671e-01 -5.747523e-01 -6.411171e-01 -1.356568e-01 -1.808869e-01
## [4496] -1.659628e-01 -9.998402e-02 1.496782e+00 -1.224665e+00 1.438980e+00
## [4501] -6.026364e-01 6.296544e-01 -5.318421e-01 -6.735522e-02 -7.709691e-01
## [4506] -2.530919e-01 7.496625e-02 -2.917220e-01 -5.397572e-02 1.737097e+00
## [4511] -1.184018e+00 1.298555e-01 -4.650911e-01 5.492108e-01 -3.838947e-01
## [4516] 4.249387e-01 -4.004126e-01 -1.391624e-01 1.023921e-01 -1.537523e-01
## [4521] 5.473572e-01 4.064871e-01 -1.257880e+00 8.548287e-01 -8.077055e-01
## [4526] 5.701603e-01 -7.480573e-01 1.269650e+00 -2.317384e-01 -3.070084e-01
## [4531] 3.147776e-03 -1.079920e-01 2.785119e-01 7.707721e-01 -9.090721e-01
## [4536] 8.218275e-01 -9.600669e-01 5.302586e-01 -7.541756e-01 4.809129e-01
## [4541] 7.864504e-01 -1.092811e-01 8.129160e-01 -2.984317e-01 1.137851e+00
## [4546] 2.011381e-01 -9.352219e-01 8.827570e-01 -8.697722e-01 5.244665e-01
## [4551] -8.728996e-01 -4.365137e-01 3.272357e-01 -2.739291e-01 7.660362e-01
## [4556] -1.371269e-01 -3.759476e-01 3.159133e-01 -1.346519e+00 1.849712e+00
## [4561] -6.887256e-01 4.583716e-01 -5.838748e-01 1.989124e+00 -4.239909e-02
## [4566] -4.758965e-01 3.112546e-01 -4.964089e-01 1.327441e-01 5.821735e-01
## [4571] -1.238664e+00 1.076415e+00 -7.045892e-01 3.478191e-01 -9.048294e-01
## [4576] 1.107070e+00 7.448433e-02 -4.204190e-01 7.329507e-01 -3.962097e-01
## [4581] 2.318620e-01 -3.482687e-01 -1.176490e+00 1.138903e+00 -1.004341e+00
## [4586] 5.642394e-01 -6.506940e-01 -3.057822e-01 -1.860425e-02 -1.664710e-01
## [4591] 1.983984e-01 -1.799180e-01 -1.155074e-01 -1.263006e-01 -1.294075e+00
## [4596] 1.756057e+00 -7.454993e-01 4.156702e-01 -1.033090e+00 3.873308e-01
## [4601] -7.161468e-01 -4.452966e-01 -1.632573e-01 -1.912539e-01 -1.961015e-01
## [4606] 1.160750e+00 -1.188651e+00 5.931612e-01 -9.491202e-01 4.068372e-01
## [4611] -6.756295e-01 2.114847e+00 6.823121e-01 -3.248927e-01 1.003487e-01
## [4616] -2.133979e-01 5.213804e-01 5.383411e-01 -8.669152e-01 7.468909e-01
## [4621] -3.801766e-01 1.012480e+00 -3.162386e-01 2.760311e-01 3.104845e-01
## [4626] -5.220101e-01 1.134325e+00 -3.118788e-01 -3.900399e-01 -2.366556e-01
## [4631] -1.371821e+00 -2.293896e-01 -1.060876e-01 7.909562e-01 -8.205076e-01
## [4636] -4.921923e-01 -5.672133e-02 -9.390043e-01 -1.094143e-01 3.431943e-01
## [4641] -4.223005e-01 7.153883e-01 -1.135456e+00 -4.274660e-01 -7.514720e-01
## [4646] 6.030048e-01 -7.716776e-01 2.831011e-01 8.571449e-01 -6.036009e-01
## [4651] 2.700426e-01 1.091902e-01 -1.910803e-01 -1.195207e-01 -1.493895e+00
## [4656] -8.587118e-02 -1.569296e+00 3.362563e-01 -1.278870e+00 -2.254989e-01
## [4661] -8.044852e-01 -1.547672e+00 1.469088e-01 -4.679644e-01 2.596320e-01
## [4666] -4.733073e-01 -2.078637e+00 1.395600e+00 -3.859863e-01 9.456259e-01
## [4671] -6.111020e-01 2.108970e+00 2.246260e+00 -9.502164e-01 1.309311e+00
## [4676] -7.241452e-01 6.316860e-01 2.500996e+00 -2.465340e+00 2.489162e+00
## [4681] -7.550693e-01 7.398185e-01 -2.048477e-01 8.335798e-01 6.955977e-01
## [4686] -1.357274e+00 2.349457e+00 -2.591404e-01 1.190088e+00 2.579328e+00
## [4691] 3.227629e-01 7.773818e-01 -9.724263e-01 6.180026e-01 -8.118068e-01
## [4696] 7.261196e-01 5.804399e-01 -1.112398e+00 2.482051e-01 -9.874407e-01
## [4701] 8.078708e-01 1.946997e+00 -2.268243e+00 2.030555e+00 -1.220146e+00
## [4706] 2.110002e-01 -1.324571e+00 2.516631e+00 1.171948e+00 -1.538107e+00
## [4711] 4.098739e-01 2.151934e-01 1.110277e+00 1.704991e+00 -3.008285e+00
## [4716] 8.408061e-01 -1.416941e+00 -2.477824e-02 -1.101551e+00 2.599755e+00
## [4721] 2.710360e-02 -2.245584e+00 2.600182e+00 -1.443274e+00 -4.838743e-01
## [4726] 1.539642e+00 -2.549392e+00 1.672697e+00 -2.086867e-01 2.617232e-01
## [4731] -1.636669e+00 5.770590e-01 8.830740e-01 -2.009827e+00 2.205475e-01
## [4736] -5.972383e-01 1.936871e-02 1.313890e+00 -1.740988e+00 2.797736e+00
## [4741] -1.154480e+00 1.721945e-01 -1.451475e+00 2.383076e-01 1.771625e+00
## [4746] -2.088654e+00 1.302525e+00 -7.401477e-01 4.253764e-01 9.956694e-01
## [4751] -1.589536e+00 1.704969e+00 9.595200e-02 1.495436e-01 -1.493065e+00
## [4756] -4.338623e-01 7.616593e-01 -1.614358e+00 1.493290e+00 -1.371695e-01
## [4761] -2.823354e-01 4.314348e-01 -5.909741e-01 -1.731522e-01 -9.950155e-01
## [4766] 8.198568e-01 -5.560618e-01 2.155746e-01 8.206478e-03 -4.359183e-01
## [4771] 1.213995e+00 -1.615999e-02 3.277276e-02 3.888319e-01 -1.029535e+00
## [4776] 3.460375e-01 -8.686627e-01 7.916066e-01 -6.149735e-01 -4.358826e-01
## [4781] -4.575424e-01 -5.522408e-01 6.270503e-01 -1.461657e-01 5.736865e-02
## [4786] 3.505978e-01 -1.150481e+00 4.398722e-01 -1.197805e+00 8.379706e-01
## [4791] -6.806420e-01 5.895652e-01 -4.450733e-01 -6.905031e-01 1.671364e-01
## [4796] -3.363310e-01 1.701402e-01 1.034119e+00 -1.295423e+00 5.875658e-01
## [4801] -1.149409e+00 5.045761e-01 -8.838407e-01 1.222700e-02 2.169151e-01
## [4806] -7.936569e-01 1.114398e-01 -2.607594e-01 5.056735e-01 4.180909e-01
## [4811] -1.132829e+00 2.082712e+00 -1.489231e+00 8.780739e-01 -1.025223e+00
## [4816] 1.660939e+00 1.139687e+00 -4.618422e-01 5.085283e-01 -4.376541e-01
## [4821] 1.242183e-02 1.152921e+00 -1.172258e+00 1.154514e+00 -1.578418e+00
## [4826] 4.928285e-01 -9.562850e-01 -5.493041e-02 1.235939e+00 -8.153328e-01
## [4831] 2.336262e+00 -4.562697e-01 4.911760e-01 -2.623321e-01 -1.351313e+00
## [4836] 1.522356e+00 -1.436337e+00 4.786793e-01 -1.146056e+00 7.134748e-01
## [4841] 1.576656e+00 -1.124133e+00 1.115920e+00 -1.303687e-01 1.091752e-01
## [4846] 1.224108e+00 -1.315926e+00 2.674254e+00 -1.182266e+00 5.015501e-01
## [4851] -1.015145e+00 3.312303e-01 1.834259e-01 -1.025601e+00 8.694628e-01
## [4856] -3.247916e-01 3.349187e-01 1.394332e+00 -1.303761e+00 9.852592e-01
## [4861] -1.442986e+00 5.444076e-01 -1.379157e+00 2.102726e+00 1.454695e-01
## [4866] -9.368848e-01 1.457466e+00 -3.266682e-01 6.560599e-01 2.155114e+00
## [4871] -1.025431e+00 3.980390e-01 -1.658389e+00 6.185605e-01 -1.333509e+00
## [4876] 5.627397e-01 1.329348e-01 -7.435923e-01 9.680892e-01 -5.978974e-01
## [4881] -4.339164e-01 1.199124e+00 -1.415677e+00 2.166064e-03 -1.424563e+00
## [4886] 5.297518e-01 -1.295891e+00 7.295601e-02 -2.357734e-02 -1.082372e+00
## [4891] 2.801378e-01 -4.971133e-01 8.513514e-01 1.204834e+00 -1.272191e+00
## [4896] 8.983497e-01 -1.396831e+00 7.367283e-01 -1.125134e+00 1.241108e+00
## [4901] 1.059650e+00 -9.836805e-01 9.176736e-02 -2.839045e-01 6.625793e-01
## [4906] 1.022585e+00 -9.326997e-01 2.667950e-01 -5.588767e-01 5.438387e-01
## [4911] -4.342692e-01 -2.462069e-01 1.198788e+00 -5.493564e-01 -1.228578e-01
## [4916] -2.434538e-02 6.609417e-02 -1.373801e-01 -6.589575e-01 -1.088055e-01
## [4921] -2.693614e-01 4.379366e-01 -6.396089e-01 -5.633917e-01 -8.738952e-01
## [4926] -5.509596e-01 4.907899e-01 -3.016204e-01 -9.820677e-01 6.620248e-01
## [4931] -5.959595e-01 -3.681108e-02 -3.346427e-01 5.693574e-01 -6.688979e-01
## [4936] 5.935722e-02 7.306035e-01 -6.071439e-01 4.472967e-01 -2.736950e-01
## [4941] -3.835181e-01 1.351519e+00 -8.916728e-01 -3.635865e-02 -9.042888e-01
## [4946] 2.331725e-01 -6.513071e-01 2.586262e-01 -3.526376e-01 -1.094622e+00
## [4951] 5.665473e-01 -1.126781e+00 -2.019754e-01 -1.459376e-01 -1.153401e+00
## [4956] -4.407196e-01 7.416161e-01 5.217617e-01 -8.333328e-01 2.939358e+00
## [4961] 8.988818e-01 -9.299481e-01 1.027658e+00 6.020560e-01 7.248850e-01
## [4966] 2.154805e+00 -1.793756e+00 1.630525e+00 1.490638e-01 7.048804e-01
## [4971] -4.641599e-01 -6.725835e-01 1.060370e+00 -1.034354e+00 7.116242e-01
## [4976] 3.877787e-01 5.077914e-01 6.903024e-01 -8.261885e-01 4.717953e-01
## [4981] -1.022010e+00 6.459901e-01 -9.341016e-01 2.193842e-01 4.806220e-01
## [4986] -6.136322e-01 4.067663e-01 -8.425606e-01 1.293392e+00 4.837109e-01
## [4991] -2.194097e+00 1.464987e+00 -7.540503e-01 1.562585e-01 -1.060718e+00
## [4996] 1.285115e+00 4.665376e-01 -1.283896e+00 2.310983e-01 8.574835e-01
## [5001] 1.149414e+00 3.195502e-01 -8.233847e-01 1.439125e+00 -7.003757e-01
## [5006] 1.686865e+00 -8.013466e-01 1.062663e+00 -4.836696e-01 -1.611755e+00
## [5011] 1.152662e+00 -1.652714e-01 -1.576682e-01 7.413209e-01 -1.233868e+00
## [5016] 5.085318e-01 -7.579515e-01 5.105157e-01 -1.057618e+00 -5.910254e-01
## [5021] -3.099223e-01 -6.903913e-01 -4.176566e-01 1.157295e-01 1.441155e-01
## [5026] 2.775198e-01 -2.032395e+00 2.840003e+00 -2.001873e-01 2.517437e-01
## [5031] -1.293187e+00 1.584195e+00 -4.857690e-01 -1.591502e+00 -1.556500e-01
## [5036] 3.347368e-01 7.635300e-01 1.864448e+00 -1.781009e+00 6.046491e-01
## [5041] -3.810968e-01 1.499906e-01 -8.858868e-01 9.663838e-02 1.392708e+00
## [5046] -1.357832e+00 2.764995e-01 7.097739e-02 -2.135859e-01 1.143413e+00
## [5051] -6.405441e-01 1.252218e-02 -1.545226e+00 1.062791e+00 -1.247370e+00
## [5056] -1.965800e-01 5.037206e-01 -9.987018e-01 3.590110e-01 -6.044623e-01
## [5061] 1.443275e+00 -1.269078e+00 -1.700254e+00 2.326936e+00 -1.315775e+00
## [5066] 1.106072e+00 -1.653059e+00 1.242611e-01 2.393105e-01 -1.189277e+00
## [5071] 1.462457e+00 -6.909530e-01 7.810274e-01 2.460794e+00 -1.752360e+00
## [5076] 9.925410e-01 -1.775924e+00 1.276293e+00 -1.283221e+00 8.133772e-01
## [5081] 3.658039e-01 -1.267288e+00 6.978246e-01 -1.360710e+00 -1.082608e+00
## [5086] 1.281179e+00 -2.518385e+00 1.141522e+00 -1.657519e+00 5.805646e-01
## [5091] -1.822098e+00 2.817909e-02 -8.598504e-01 -1.431472e+00 5.799159e-01
## [5096] -1.289586e+00 -2.377961e-01 2.093885e+00 -2.245257e+00 1.536332e+00
## [5101] -1.174831e+00 1.417365e+00 -7.774674e-01 2.338542e+00 -9.559486e-02
## [5106] -9.988091e-01 2.050948e-01 -7.332026e-01 1.625914e+00 1.223011e+00
## [5111] -8.836655e-01 1.524669e+00 -7.746604e-01 1.255096e+00 -8.772853e-01
## [5116] 5.224655e-01 9.794197e-01 -1.098997e+00 2.648368e+00 -1.501435e-01
## [5121] 1.668355e+00 2.458404e-01 -4.796016e-01 8.975723e-01 -6.174998e-01
## [5126] 1.080075e+00 -1.122960e+00 1.794801e-01 2.220821e+00 -1.669740e+00
## [5131] 1.627142e+00 6.392528e-01 -1.518067e+00 1.186227e-01 -1.712823e+00
## [5136] 2.940102e+00 -3.936853e-01 1.318111e+00 -7.062095e-01 2.098615e+00
## [5141] -9.650829e-02 -1.603528e+00 1.292780e+00 -7.090288e-01 2.033863e-01
## [5146] 1.365759e+00 -1.631491e+00 6.199662e-01 -8.837002e-01 1.376289e+00
## [5151] -1.277107e+00 2.070626e-01 9.616899e-01 -1.623557e+00 1.862198e+00
## [5156] -1.513414e+00 1.240877e+00 -8.776248e-01 -1.375956e+00 1.010476e+00
## [5161] -8.653228e-01 8.829242e-01 -1.310275e+00 -2.057820e-01 4.246086e-01
## [5166] -1.396472e+00 1.025453e+00 -8.758156e-01 2.957406e-01 -1.717003e-01
## [5171] -2.367810e+00 2.458800e+00 -9.214412e-01 1.224119e+00 -1.552744e+00
## [5176] 7.669054e-01 -6.422202e-01 -1.887668e+00 1.338445e-01 -9.205296e-01
## [5181] -2.697318e-01 3.076456e-01 -1.026711e+00 1.609174e-01 -1.253144e+00
## [5186] 1.383318e+00 -1.316248e+00 1.622191e+00 1.527301e+00 -1.531078e+00
## [5191] 1.499243e+00 -1.405678e-01 1.371885e+00 5.094351e-01 -1.300383e+00
## [5196] 9.937935e-01 -5.807957e-01 1.138054e+00 -6.263010e-01 -3.065530e-01
## [5201] -1.877885e-01 -4.770679e-01 8.665525e-01 -4.921395e-01 -4.572730e-02
## [5206] -3.037045e-01 -1.465363e+00 -1.451756e-01 -4.358590e-01 1.046192e+00
## [5211] -7.252468e-01 -3.579998e-01 -1.717817e-02 -5.405052e-01 3.452611e-02
## [5216] 4.348041e-01 -2.224989e-01 9.210078e-01 -9.899733e-01 -5.521575e-01
## [5221] -8.341453e-01 1.098836e+00 -8.229661e-01 -4.879108e-01 -3.330676e-01
## [5226] -5.991580e-01 4.080661e-01 -2.023258e-01 -6.432081e-01 8.579111e-02
## [5231] -1.720972e+00 2.050998e-01 -1.294476e+00 9.944517e-01 -1.263214e+00
## [5236] -9.252378e-01 -9.558286e-01 -1.240944e+00 1.264950e-04 -6.612429e-01
## [5241] 8.766480e-02 -2.154928e-01 -1.859372e+00 1.427761e+00 -2.263128e-01
## [5246] 9.183231e-01 -8.791323e-01 2.295066e+00 1.701382e+00 -1.372009e+00
## [5251] 1.148404e+00 -4.125238e-01 8.694133e-01 2.289997e+00 -2.818840e+00
## [5256] 2.663893e+00 -7.972080e-01 5.876650e-01 -7.616618e-01 5.995465e-01
## [5261] 3.889383e-01 -1.634279e+00 1.299875e+00 -4.571600e-02 7.820004e-01
## [5266] 2.577123e+00 -8.546746e-01 9.220709e-01 -1.386162e+00 7.832551e-01
## [5271] -1.149124e+00 8.462435e-01 1.230984e+00 -1.051046e+00 5.850080e-01
## [5276] -1.892244e-01 7.187155e-01 1.518216e+00 -1.445043e+00 1.850508e+00
## [5281] -9.768534e-01 5.566898e-01 -9.285095e-01 2.033870e+00 1.399906e+00
## [5286] -1.421969e+00 1.533354e+00 -4.524384e-02 1.296685e+00 4.101947e-01
## [5291] -1.900793e+00 1.105069e+00 -1.331489e+00 3.702397e-01 -1.327107e+00
## [5296] 1.779086e+00 5.731837e-01 -1.928765e+00 1.963452e+00 -1.227755e+00
## [5301] -4.013260e-01 2.132536e+00 -1.881121e+00 1.509755e+00 -1.338038e+00
## [5306] 4.255116e-01 -1.560677e+00 1.790991e+00 6.376134e-01 -1.528006e+00
## [5311] 5.391604e-01 -4.286255e-01 1.645208e-01 8.616620e-01 -1.555165e+00
## [5316] 1.736125e+00 -1.208453e+00 6.503827e-02 -1.728970e+00 6.826458e-01
## [5321] 6.312592e-01 -2.241788e+00 9.143625e-01 -1.670615e-01 7.472537e-02
## [5326] 7.883410e-01 -1.644049e+00 2.622753e+00 -9.577197e-01 1.191819e-01
## [5331] -1.554122e+00 1.047211e-02 6.535503e-01 -1.926852e+00 1.102268e+00
## [5336] -3.268097e-01 7.602172e-01 8.301630e-01 -2.051173e-02 1.846970e+00
## [5341] -1.288154e-01 3.283546e-01 -2.471255e-02 -1.467208e-01 4.016378e-02
## [5346] -3.883534e-01 6.974437e-01 2.101930e-02 -1.862578e-01 -2.166562e-01
## [5351] -3.046134e-01 7.298859e-01 -3.135901e-01 3.840963e-01 -3.109973e-01
## [5356] 4.970673e-01 -4.254280e-01 -5.494954e-01 -5.067950e-02 4.328270e-02
## [5361] -9.427319e-02 -1.365924e-01 -8.254087e-01 7.987970e-01 -3.955034e-01
## [5366] 9.436482e-02 -4.355061e-01 6.045159e-01 -5.577284e-01 -6.633418e-01
## [5371] 1.877033e-01 -3.840754e-01 -6.189012e-01 4.518690e-02 -1.043098e+00
## [5376] 2.481305e-01 -4.922995e-01 1.520068e-02 -6.582297e-01 -6.349001e-01
## [5381] -7.873498e-01 -6.282413e-01 -1.187712e-01 -4.793438e-01 -3.494476e-01
## [5386] 7.244587e-01 1.967570e+00 -1.168774e+00 -6.641446e-02 -4.329823e-01
## [5391] -1.112617e+00 -2.311188e+00 5.035291e+00 5.560637e-01 2.543921e+00
## [5396] -1.380598e+00 4.288407e-02 5.581974e+00 -2.725322e+00 -1.532457e+00
## [5401] 1.115378e+00 -1.011236e+00 9.900847e-01 -1.910848e+00 2.577621e+00
## [5406] -6.568062e-01 -6.142813e-01 -2.998447e-01 -7.203685e-01 2.141906e-02
## [5411] -4.590417e-01 -8.965329e-01 1.052067e+00 -4.302254e-01 4.520387e-01
## [5416] -1.187698e+00 -6.581850e-01 -9.094931e-01 -1.840010e+00 -6.177218e-01
## [5421] -1.770284e-01 -1.372721e-01 4.205755e-01 -2.004653e+00 7.582881e-01
## [5426] -1.955616e+00 9.910084e-01 -1.565602e+00 4.941127e-02 -1.680715e+00
## [5431] -1.135622e+00 6.478518e-01 -8.558093e-01 -1.786372e-01 1.977600e+00
## [5436] -1.211599e+00 -5.343873e-01 -1.283833e+00 -6.264522e-01 -1.275070e+00
## [5441] 2.606237e+00 -9.487569e-01 -9.359598e-01 -2.341751e-01 -5.183535e-01
## [5446] 9.905838e-01 -1.701860e-01 -9.576146e-01 1.888668e+00 -2.376074e-01
## [5451] 1.506217e+00 -4.635807e-02 1.297018e+00 1.041685e+00 -7.663949e-01
## [5456] 8.289487e-01 1.552106e+00 -7.624166e-01 1.413695e+00 -3.224444e-01
## [5461] 2.028000e+00 -9.683709e-01 1.032913e+00 -6.763038e-01 6.336950e-01
## [5466] 2.826204e+00 -1.444546e+00 1.296096e+00 1.303520e+00 5.445863e-01
## [5471] 1.102270e-01 -7.596688e-01 1.424836e+00 -2.293292e-01 -1.595048e-01
## [5476] -4.911862e-01 2.330593e-02 3.157988e-01 -8.517610e-01 1.574618e+00
## [5481] -1.630847e+00 -1.308456e+00 9.536729e-02 -1.994249e+00 1.707304e+00
## [5486] 2.788641e-01 9.902076e-01 -6.256272e-01 1.315054e+00 6.933354e-01
## [5491] -2.375727e+00 5.327117e-01 -1.174941e+00 2.063415e+00 5.030014e-01
## [5496] -1.768615e+00 4.973755e-01 -1.107917e+00 7.007810e-01 -2.297252e+00
## [5501] 1.551719e+00 -1.179273e+00 -4.948611e-01 2.234200e+00 7.825419e-03
## [5506] 1.651045e+00 1.476165e-01 -1.470937e+00 -1.321154e-01 -2.230536e+00
## [5511] 1.944295e+00 -1.156946e+00 -9.662397e-01 4.476416e-01 1.738711e+00
## [5516] 1.903809e+00 1.314923e+00 9.422671e-01 -8.693833e-01 -3.540566e-01
## [5521] 1.101339e+00 -1.301524e+00 1.326382e+00 -2.308211e+00 -1.451775e-01
## [5526] -8.710296e-01 5.493157e-01 6.076010e-01 -2.989582e-01 -9.147276e-02
## [5531] -1.725360e-01 3.906012e-01 1.012440e+00 -8.357821e-01 5.052054e-01
## [5536] -1.472425e+00 8.027862e-01 9.336526e-01 -6.067284e-01 4.070967e-01
## [5541] -1.245541e+00 -5.726360e-01 -7.424249e-01 -1.146668e+00 1.153629e-03
## [5546] -4.053222e-01 9.451665e-01 -3.257097e-01 7.546241e-02 -4.352483e-01
## [5551] 8.804767e-02 -1.791726e-02 -1.039739e-01 8.050752e-01 1.498395e-01
## [5556] -1.388378e+00 1.042982e+00 -7.202575e-01 7.719029e-01 -5.606875e-01
## [5561] -7.906050e-01 -6.883966e-01 -1.836579e-01 -1.927401e-01 -2.765515e-01
## [5566] -2.057208e-01 1.750573e+00 -1.486774e+00 1.796157e+00 -7.571904e-01
## [5571] 8.106418e-01 -6.586348e-01 -2.312838e-01 -1.043116e+00 -2.891181e-01
## [5576] 1.051520e-01 -2.042384e-01 3.740348e-01 2.278475e+00 -1.523061e+00
## [5581] -1.178688e-01 -6.177690e-01 6.009776e-01 -6.111413e-01 3.928153e-01
## [5586] -6.147193e-01 -1.857706e-01 2.696184e-02 -2.153221e-01 6.322389e-01
## [5591] 5.699653e-01 -1.508478e+00 1.333879e+00 -1.096159e+00 6.616268e-01
## [5596] -9.546251e-01 1.807651e+00 -9.593881e-02 -5.225106e-01 3.988438e-02
## [5601] -1.773726e-02 -3.573083e-01 1.462351e+00 -1.183898e+00 1.800924e+00
## [5606] -1.451103e+00 6.701554e-01 -1.236031e+00 7.952173e-01 1.102057e+00
## [5611] -3.171763e-01 1.408360e+00 -3.807263e-01 1.011460e+00 6.047333e-02
## [5616] -1.074978e+00 1.180431e+00 -1.248517e+00 3.468409e-01 -1.161348e+00
## [5621] -3.929284e-01 5.011661e-01 -4.470173e-01 8.414361e-01 -5.986261e-01
## [5626] -3.549015e-01 6.128663e-01 -1.753971e+00 2.294598e+00 -9.032365e-01
## [5631] 5.923427e-01 -6.811503e-01 2.049680e+00 -9.657358e-02 -7.761482e-01
## [5636] 6.138219e-01 -5.931096e-01 1.775335e-01 1.177312e+00 -1.544789e+00
## [5641] 1.690140e+00 -1.100125e+00 3.889827e-01 -1.102651e+00 1.704414e+00
## [5646] 5.507758e-02 -4.845721e-01 1.346221e+00 -6.404320e-01 7.156491e-01
## [5651] -4.534587e-01 -1.380042e+00 9.934914e-01 -1.337129e+00 8.050603e-01
## [5656] -9.942771e-01 -2.033569e-01 1.705917e-01 5.691556e-02 4.561809e-01
## [5661] 9.775620e-02 -2.718222e-01 -3.305754e-01 -1.441649e+00 1.766085e+00
## [5666] -9.998747e-01 4.126574e-01 -1.253477e+00 -2.347528e-01 -8.689736e-01
## [5671] -4.739117e-01 1.082330e-01 -2.563185e-01 -1.926425e-01 1.733508e+00
## [5676] -1.181093e+00 1.853442e-01 -1.060113e+00 6.271721e-01 -8.906719e-01
## [5681] 3.151418e+00 9.025915e-01 -3.143739e-01 3.618178e-01 -4.346911e-01
## [5686] -1.507913e-02 8.062502e-02 -7.971384e-01 3.495824e-01 -1.418373e+00
## [5691] 1.278137e+00 -1.367461e+00 6.537514e-01 -3.466916e-01 -1.385920e+00
## [5696] 1.571400e+00 3.249344e-02 3.441076e-01 -5.091070e-01 -1.986414e+00
## [5701] 4.283123e-01 -8.649905e-01 1.138000e+00 -1.347681e+00 1.119627e+00
## [5706] 1.254780e+00 -1.534520e+00 5.267086e-01 -5.493550e-01 -4.051403e-01
## [5711] -5.763603e-02 -1.469594e+00 8.043328e-01 -1.365528e+00 1.483894e+00
## [5716] -1.288692e+00 5.187642e-01 9.354326e-01 -1.102565e+00 2.089376e+00
## [5721] -9.914634e-02 -9.067183e-01 1.573603e-02 -1.891150e+00 1.939261e-01
## [5726] -1.761213e+00 9.613165e-01 -1.546356e+00 1.081289e-01 -3.245331e-01
## [5731] -2.406706e+00 1.105918e+00 -1.271388e+00 1.008141e-01 6.456169e-01
## [5736] -2.114256e+00 1.479214e+00 -7.607174e-01 1.155534e+00 -1.422748e+00
## [5741] 6.701493e-01 8.150243e-01 -2.444632e+00 1.501762e+00 -1.132113e+00
## [5746] 2.729321e-02 1.965351e+00 -1.216658e+00 1.460574e+00 -1.059422e+00
## [5751] 1.068450e+00 -1.310575e+00 2.130205e+00 7.181906e-01 -2.799898e+00
## [5756] 3.078607e+00 6.787480e-01 5.775104e-01 1.862283e+00 -3.484904e-01
## [5761] 2.097318e+00 -1.294895e+00 1.111583e+00 -1.408106e+00 1.177860e+00
## [5766] 2.104338e+00 -1.482451e+00 2.312137e+00 2.738209e-01 5.540129e-01
## [5771] 2.174220e+00 -1.672170e+00 1.127541e+00 -1.380791e+00 1.293599e+00
## [5776] -1.212190e+00 -5.875304e-01 -5.963861e-02 -2.076403e+00 1.033915e-01
## [5781] -1.823069e-01 7.393543e-01 2.444719e+00 -2.655146e+00 9.512084e-01
## [5786] -9.283403e-01 9.418360e-01 -1.865231e+00 2.631810e+00 1.257499e+00
## [5791] -2.338664e+00 1.594180e+00 -1.334230e+00 -2.136515e-01 1.130549e+00
## [5796] -1.957993e+00 1.946357e+00 -1.544696e+00 8.053056e-01 -1.336631e+00
## [5801] 1.316804e+00 3.185241e-01 -2.452099e+00 -6.222039e-01 -9.054388e-01
## [5806] 9.766367e-01 1.395516e+00 -2.282540e+00 2.041039e+00 -1.445789e+00
## [5811] 8.551963e-01 -1.729050e+00 1.268657e+00 2.402083e+00 -2.021880e+00
## [5816] 8.402707e-01 -6.019612e-02 -2.627951e-01 2.729979e-01 -1.281068e+00
## [5821] 1.108733e+00 -8.090052e-01 8.971701e-01 -1.606753e+00 -1.056955e+00
## [5826] 1.795512e+00 -1.865730e+00 2.279550e+00 2.943377e-01 2.271915e-01
## [5831] -7.044485e-02 -9.881487e-01 4.888198e-01 -9.227464e-01 1.012933e+00
## [5836] -8.140371e-01 5.069478e-01 9.611544e-01 -6.905579e-01 1.000997e+00
## [5841] -3.885588e-01 2.294380e-01 5.256990e-01 -1.373650e+00 7.085507e-01
## [5846] -9.417540e-01 1.023372e+00 -8.472308e-01 2.588998e-01 3.625281e-01
## [5851] -6.219608e-01 2.036869e-01 -1.445755e-01 -2.245812e-02 1.545455e+00
## [5856] -1.527386e+00 1.426508e+00 -1.038821e+00 8.859187e-01 -9.797098e-01
## [5861] -1.484664e-01 -3.051773e-01 -8.725724e-01 6.438839e-01 -4.676511e-01
## [5866] -5.947163e-02 4.163205e-01 -1.521911e+00 1.099631e-01 -1.163143e+00
## [5871] 8.619155e-01 -1.085664e+00 1.255865e-02 1.262805e+00 -8.621837e-01
## [5876] 6.843612e-01 -5.962188e-01 -6.848408e-01 4.747158e-01 -1.501076e+00
## [5881] 2.010256e+00 -1.016076e+00 9.914414e-01 -1.010236e+00 1.657896e+00
## [5886] 1.433730e+00 -8.706161e-01 5.878335e-01 -2.097560e-01 1.010683e-01
## [5891] 9.746725e-01 -1.523636e+00 9.267810e-01 -1.104485e+00 9.528680e-01
## [5896] -9.916072e-01 7.007267e-01 -6.143964e-02 -1.035368e+00 1.085423e+00
## [5901] -6.491299e-02 8.702816e-01 8.738122e-01 -1.841270e+00 1.504376e+00
## [5906] -1.080111e+00 8.942044e-01 -1.144136e+00 8.334389e-01 1.209033e+00
## [5911] -1.179707e+00 9.257771e-01 1.946128e-02 -1.250232e-01 7.198707e-01
## [5916] -1.895155e+00 3.128648e+00 -1.297600e+00 8.208102e-01 -1.171389e+00
## [5921] 1.902223e+00 6.543448e-01 -1.189651e+00 -4.639877e-01 -3.414800e-01
## [5926] 2.927736e-01 1.371276e+00 -1.748709e+00 1.466152e+00 -1.366820e+00
## [5931] 8.287544e-01 -1.278657e+00 7.120160e-01 1.086359e+00 -1.250024e+00
## [5936] 1.162162e+00 -4.236479e-01 5.325269e-01 1.268793e+00 -1.790246e+00
## [5941] 2.937123e-01 -1.332146e+00 8.977603e-01 -1.194653e+00 1.344886e+00
## [5946] 4.264810e-01 -1.299612e+00 6.164846e-01 -4.835743e-01 9.812275e-01
## [5951] 1.114731e+00 -1.845407e+00 1.832465e+00 -1.333807e+00 8.513911e-01
## [5956] -1.294507e+00 7.778688e-01 -3.755616e-01 -1.275825e+00 6.913629e-02
## [5961] -3.922014e-01 3.136767e-01 3.253968e-01 -1.840888e+00 1.503742e+00
## [5966] -1.170771e+00 8.279574e-01 -1.331381e+00 1.281268e+00 1.633920e-01
## [5971] -1.363027e+00 -2.267675e-01 8.021122e-02 1.584372e+00 1.127439e+00
## [5976] -1.432925e+00 8.089703e-01 -8.084307e-01 9.646593e-01 -1.375620e+00
## [5981] -4.000478e-01 -1.080738e-01 -5.582971e-01 -1.021375e-01 -1.770517e-01
## [5986] 1.337374e+00 1.564321e-01 -2.268866e+00 2.084994e+00 -8.115482e-01
## [5991] 8.145367e-01 -1.394871e+00 1.262137e+00 -4.806135e-01 -1.095075e+00
## [5996] -2.491311e-01 -2.601000e-01 -1.714276e-02 2.020937e+00 -1.444721e+00
## [6001] 1.886897e+00 -9.133647e-01 1.117019e+00 -1.066175e+00 8.783000e-01
## [6006] -5.521735e-01 -9.402613e-01 9.260508e-01 -3.299819e-01 -7.204367e-01
## [6011] 2.124294e+00 -1.864304e+00 8.897214e-01 -1.095779e+00 1.230590e+00
## [6016] -1.214890e+00 1.021463e+00 5.266221e-01 -7.427125e-01 7.946664e-01
## [6021] -5.503007e-01 5.811269e-01 7.214249e-01 -1.890156e+00 7.548069e-01
## [6026] -1.525629e+00 7.846005e-01 -1.559402e+00 9.316914e-01 -6.750922e-01
## [6031] -1.235925e+00 4.661911e-01 -8.868039e-01 6.860790e-01 1.159492e+00
## [6036] -7.095558e-01 1.952429e+00 -1.301558e+00 1.151106e+00 -1.344700e+00
## [6041] 5.810032e-01 1.221710e+00 -7.415958e-01 7.682796e-01 -5.099774e-01
## [6046] 1.189586e+00 6.449854e-01 -1.033275e+00 8.553596e-01 -1.318873e+00
## [6051] 1.769218e+00 -1.381572e+00 -6.138106e-01 1.561334e+00 -2.344623e-01
## [6056] 9.516311e-01 3.077639e-01 -2.729828e-01 9.136254e-01 -1.635131e+00
## [6061] 1.881376e+00 -7.966378e-01 9.670220e-01 -1.293837e+00 2.798154e+00
## [6066] 1.056104e+00 -9.214110e-01 9.954071e-01 -7.716824e-01 -2.887343e-01
## [6071] 1.421157e-01 -2.079075e+00 1.231149e+00 -8.620604e-01 8.256699e-01
## [6076] -1.581695e+00 6.600697e-01 1.711609e-02 -1.176095e+00 1.198298e+00
## [6081] -3.074209e-01 -2.322949e-01 -6.520646e-02 -1.590396e+00 1.239602e+00
## [6086] -1.340520e+00 8.781810e-01 -1.126387e+00 8.546013e-02 2.882346e-01
## [6091] -1.073159e+00 9.237234e-02 -6.291165e-01 -1.061122e+00 2.512127e-01
## [6096] -2.060366e+00 2.639648e+00 -1.009825e+00 1.194208e+00 -1.610814e+00
## [6101] 1.145468e+00 -6.609722e-01 -1.242218e+00 4.769791e-01 -4.782979e-01
## [6106] -3.046173e-02 1.184234e+00 -1.650239e+00 1.999161e-01 -1.364943e+00
## [6111] 1.040913e+00 -1.077988e+00 1.992392e+00 1.044861e+00 -5.611896e-01
## [6116] 3.387392e-01 1.831198e-01 7.167639e-01 1.756838e+00 -5.462080e-01
## [6121] -1.824162e-01 -1.184281e+00 1.238056e+00 -1.213528e+00 -3.439613e-02
## [6126] 9.831672e-01 -1.331718e+00 7.370527e-01 2.999121e-01 5.345935e-01
## [6131] -1.265708e-01 -1.475153e+00 9.921998e-01 -1.187925e+00 1.228745e+00
## [6136] -1.391013e+00 -6.052329e-01 3.928566e-01 -1.729057e+00 2.065001e+00
## [6141] -5.231205e-01 5.548135e-01 1.337552e+00 -1.441174e+00 8.579319e-01
## [6146] -1.470728e+00 1.278640e+00 -1.369672e+00 2.531768e-01 4.375406e-02
## [6151] -1.889883e+00 6.478089e-01 -1.196376e+00 -1.028004e+00 1.248899e+00
## [6156] -2.458581e+00 1.154054e+00 -1.540906e+00 6.922266e-01 -1.784297e+00
## [6161] -5.328065e-01 -3.181906e-01 -2.157356e+00 8.715771e-01 -1.009058e+00
## [6166] -1.001369e-01 1.152192e+00 -1.781191e+00 3.292375e+00 -1.289967e+00
## [6171] 1.510692e+00 -1.124103e+00 3.168552e+00 1.978077e+00 -1.657345e+00
## [6176] 1.325395e+00 6.319314e-02 3.407001e-01 5.967976e-01 -8.525681e-02
## [6181] 1.799346e+00 -1.757868e+00 1.335529e+00 -1.274273e+00 -3.764943e-01
## [6186] 1.636738e+00 -1.762735e+00 3.247552e+00 -4.805985e-01 4.029268e-01
## [6191] 1.288254e+00 -2.021395e+00 2.396306e+00 -1.452108e+00 8.907802e-01
## [6196] -1.805973e+00 1.028264e+00 1.701637e+00 -2.324881e+00 1.309373e+00
## [6201] 3.926002e-01 -9.678153e-01 7.006585e-01 -6.632443e-01 3.135391e+00
## [6206] -1.737270e+00 1.144270e+00 -1.331030e+00 1.363017e+00 1.330269e+00
## [6211] -2.084498e+00 1.803649e+00 -9.259717e-01 -6.272527e-02 1.500655e+00
## [6216] -2.260517e+00 2.101376e+00 -1.615931e+00 1.162957e+00 -1.810609e+00
## [6221] 9.811593e-01 1.389817e-01 -2.197732e+00 2.178861e+00 -9.228615e-01
## [6226] 1.086447e+00 1.098062e+00 -3.523991e-01 1.600201e-01 -1.654346e+00
## [6231] 1.446451e+00 -1.560035e+00 1.031237e+00 2.783008e-01 -1.704230e+00
## [6236] 2.143057e+00 -4.958526e-01 1.744643e-01 4.733060e-01 -2.534911e+00
## [6241] 4.304998e-01 -1.403158e+00 1.204265e+00 -1.709823e+00 1.837526e-01
## [6246] 7.574401e-01 -2.188677e+00 1.168555e+00 -8.623930e-01 -5.899328e-01
## [6251] 1.067805e+00 -2.381875e+00 1.469348e+00 -1.565344e+00 1.356409e+00
## [6256] -1.390497e+00 1.232064e+00 2.149133e+00 -2.251075e+00 7.254287e-01
## [6261] -2.965183e-01 1.892015e+00 2.712631e-01 -7.652585e-01 -1.648127e-01
## [6266] -3.894903e-01 4.188349e-01 -2.773019e-01 -1.601601e-01 -3.021755e-01
## [6271] 9.647902e-02 -9.298517e-03 -7.448483e-02 5.381378e-01 5.659670e-02
## [6276] -7.745008e-01 5.280246e-01 -2.847585e-01 3.690828e-01 -3.179435e-01
## [6281] -4.171004e-01 -4.683350e-01 -1.181055e-02 -1.095753e-01 -1.170819e-01
## [6286] -5.548723e-02 1.035305e+00 -9.211204e-01 8.988220e-01 -4.450462e-01
## [6291] 5.551527e-01 -3.408353e-01 -1.642273e-01 -5.422496e-01 -8.914374e-02
## [6296] 2.065361e-02 -1.346298e-01 1.290616e-01 1.242689e+00 -8.353469e-01
## [6301] 8.936891e-02 -3.591768e-01 4.179705e-01 -3.367395e-01 3.012849e-01
## [6306] -3.121573e-01 -3.411504e-02 9.219414e-02 -1.103130e-01 4.901024e-01
## [6311] 4.317122e-01 -9.626521e-01 5.675787e-01 -6.027447e-01 4.963694e-01
## [6316] -4.514505e-01 9.644828e-01 -3.355110e-01 -1.920862e-01 -9.006611e-02
## [6321] -4.596808e-02 1.449840e-01 6.813692e-01 -8.096123e-01 7.874347e-01
## [6326] -6.925689e-01 3.679009e-01 -5.532137e-01 2.601827e-01 4.611069e-01
## [6331] -1.330359e-01 4.969738e-01 -1.486519e-01 7.683806e-01 6.870195e-02
## [6336] -7.947892e-01 6.294895e-01 -6.158044e-01 3.554189e-01 -5.380627e-01
## [6341] -4.229788e-01 1.849836e-01 -2.100292e-01 5.870960e-01 -2.039644e-01
## [6346] -2.652767e-01 2.066368e-01 -1.018617e+00 1.516499e+00 -4.087889e-01
## [6351] 3.973073e-01 -3.911332e-01 1.037641e+00 -9.030088e-02 -3.171417e-01
## [6356] 1.781529e-01 -2.236645e-01 1.881177e-01 5.197236e-01 -9.647016e-01
## [6361] 1.118275e+00 -4.879019e-01 3.239341e-01 -5.716413e-01 7.545312e-01
## [6366] 5.120614e-02 -2.612236e-01 5.012026e-01 -1.633155e-01 2.553812e-01
## [6371] -3.774957e-01 -8.616266e-01 5.389477e-01 -6.627207e-01 5.236659e-01
## [6376] -4.544308e-01 -3.099852e-01 -2.939441e-01 -7.071311e-02 1.149310e-01
## [6381] -4.337897e-02 -1.637028e-01 -1.668305e-01 -9.384366e-01 9.737682e-01
## [6386] -4.148787e-01 3.356587e-01 -6.445493e-01 5.135110e-02 -6.411362e-01
## [6391] -2.888567e-01 -1.107482e-01 3.509151e-02 7.567211e-03 9.757810e-01
## [6396] -8.441485e-01 7.018271e-01 -5.776954e-01 4.009657e-01 -4.314642e-01
## [6401] 1.406627e+00 2.870502e-01 -2.091527e-01 4.336949e-02 -7.345222e-02
## [6406] 3.020651e-01 1.843342e-01# add the residuals as a new column into the HWI_grouped_species dataframe ----
NDVI_2000_2021$residuals <- residuals(all_ndvi_gam)
#save dataframe as a csv
write.csv(NDVI_2000_2021, "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/NDVI_2000_2021_residual.csv", row.names=FALSE)
NDVI_2000_2021_residuals <- read.csv("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/NDVI_2000_2021_residual.csv")
# looking at the distribution of the residuals
hist(NDVI_2000_2021$residuals)
# add a year_month column ----
# Create a new column combining year, month, and day
NDVI_2000_2021$date <- as.Date(paste(NDVI_2000_2021$year, NDVI_2000_2021$month, 1, sep="-"))
# Create a new column for year and month combination
NDVI_2000_2021$year_month <- format(NDVI_2000_2021$date, "%Y-%m")
# Convert the date column to Date format if necessary
NDVI_2000_2021$date <- as.Date(NDVI_2000_2021$date)
#save datafram as a csv
write.csv(NDVI_2000_2021, "C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/NDVI_2000_2021_residual_date.csv", row.names=FALSE)
all_ndvi <- read.csv("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/models/model_results/NDVI_2000_2021_residual_date.csv")
#plot the trend of residuals by year_month ----
ggplot() +
geom_hline(aes(yintercept = 0), col = "grey70", linetype = "dashed") +
geom_point(data = all_ndvi, aes(x = year_month, y = residuals, col = park)) +
#scale_x_continuous(limits = c(2010,2021), expand = c(0,1)) +
scale_colour_manual(name="Region",
values = manual_colors) +
xlab("Time") +
ylab("Residuals") +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
#NDVI trends in individual parks ----
#BANF ----
Banff_NDVI <- all_ndvi %>%
filter(park %in% c("BANF"))
banf_ndvi <-
ggplot() +
geom_hline(aes(yintercept = 0), col = "grey70", linetype = "dashed") +
geom_point(data = Banff_NDVI, aes(x = year, y = ndvi_monthly_mean, col = park), alpha = 0.4) +
geom_smooth(data = Banff_NDVI, aes(x = year, y = ndvi_monthly_mean, col = park),
method = "lm",
se = T) +
scale_colour_manual(name="Park",
values = manual_colors) +
xlab("Time") +
ylab("Monthly Mean NDVI") +
scale_y_continuous(limits = c(0, 0.25), expand = c(0,0.01))+
scale_x_continuous(limits = c(2000, 2021), expand = c(0,0.01),
breaks = c(2000,2005,2010,2015,2020),
labels = c(2000,2005,2010,2015,2020))+
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "none",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "white"),
plot.background = element_rect(fill = "white", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggsave(banf_ndvi, filename = "figures/case_study_banff/banf_ndvi_trend.png", width = 6, height = 4, units = "in", dpi = 600, background = "white")## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 2 rows containing non-finite outside the scale range
## (`stat_smooth()`).## Warning: Removed 2 rows containing missing values or values outside the scale range
## (`geom_point()`).We then merged the NDVI data with the HWI data.
# matching park IDs in HWI data to NDVI data----
HWI_parks$park[HWI_parks$park == "Banff"]<- "BANF"
HWI_parks$park[HWI_parks$park == "Pacific_Rim"]<- "PRIM"
HWI_parks$park[HWI_parks$park == "Waterton_Lakes"]<- "WATE"
HWI_parks$park[HWI_parks$park == "Kejimkujik"]<- "KEJI"
HWI_parks$park[HWI_parks$park == "Jasper"]<- "JASP"
HWI_parks$park[HWI_parks$park == "Forillon"]<- "FORI"
HWI_parks$park[HWI_parks$park == "Prince_Albert"]<- "PALB"
HWI_parks$park[HWI_parks$park == "Kootenay"]<- "KOOT"
HWI_parks$park[HWI_parks$park == "Glacier"]<- "GLAC"
HWI_parks$park[HWI_parks$park == "Wapusk"]<- "WAPU"
HWI_parks$park[HWI_parks$park == "Yoho"]<- "YOHO"
HWI_parks$park[HWI_parks$park == "Terra_Nova"]<- "NOVA"
HWI_parks$park[HWI_parks$park == "Mount_Revelstoke"]<- "REVE"
HWI_parks$park[HWI_parks$park == "Elk_Island"]<- "ELKI"
HWI_parks$park[HWI_parks$park == "Georgian_Bay_Islands"]<- "GBIS"
HWI_parks$park[HWI_parks$park == "Point_Pelee"]<- "PELE"
HWI_parks$park[HWI_parks$park == "Thousand_Islands"]<- "THIS"
HWI_parks$park[HWI_parks$park == "Wood_Buffalo"]<- "WOOD"
HWI_parks$park[HWI_parks$park == "Prince_Edward_Island"]<- "PEIS"
HWI_parks$park[HWI_parks$park == "Ivvavik"]<- "IVVA"
HWI_parks$park[HWI_parks$park == "Kouchibouguac"]<- "KOUC"
HWI_parks$park[HWI_parks$park == "Fundy"]<- "FUND"
HWI_parks$park[HWI_parks$park == "Nahanni"]<- "NAHA"
HWI_parks$park[HWI_parks$park == "Aulavik"]<- "AULA"
HWI_parks$park[HWI_parks$park == "Fathom_Five"]<- "FIVE"
# drop parks without polygons ----
HWI_dropped <- subset(HWI_parks, park %in% c("WATE", "ELKI", "JASP", "WOOD",
"BANF", "YOHO", "KOOT", "REVE",
"PRIM", "GLAC", "WAPU", "FUND",
"KOUC", "NOVA", "KEJI", "AULA",
"NAHA", "FIVE", "PELE", "GBIS",
"THIS", "PEIS", "FORI", "PALB", "IVVA"))
# merging HWI and NDVI 2000-2021 dataframes ----
HWI_NDVI <- merge(all_ndvi, HWI_dropped, by = c("park", "month", "year"))
# new data frame with aggregate by HWI number
hwi_ndvi <- aggregate(HWI ~ month + year + park + ndvi_monthly_mean + scaled_mean_ndvi + residuals, data = HWI_NDVI, FUN = "length")
# creating a year_month column
hwi_ndvi$year_month <- paste(hwi_ndvi$year, hwi_ndvi$month, sep = "-")
# save the data frame
saveRDS(hwi_ndvi,file ="data/hwi_ndvi.rds")# visualise HWI with NDVI residuals ----
ggplot() +
geom_hline(aes(yintercept = 0), col = "grey70", linetype = "dashed") +
geom_point(data = hwi_ndvi, aes(x = residuals, y = HWI, col = park)) +
xlab("Residuals") +
ylab("HWI") +
scale_y_log10() +
scale_colour_manual(name="Region",
values = manual_colors) +
theme_bw() +
geom_vline(xintercept = 0, linetype = "solid", color = "black", size = 0.3) +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "transparent"),
plot.background = element_rect(fill = "transparent", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## Warning in scale_y_log10(): log-10 transformation introduced infinite values.
# visualise HWI over time ---- model as a gam!
hwi_trend <-
ggplot() +
geom_point(data = hwi_ndvi, aes(x = year, y = HWI, col = park)) +
geom_smooth(data = hwi_ndvi, aes(x = year, y = HWI, col = park),
method = "gam",
formula = y ~ s(x, bs = "tp", k = 5),
method.args = list(family = "poisson"),
se = F) +
xlab("Year") +
ylab("Monthly HWIs") +
scale_colour_manual(name="Park",
values = manual_colors) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=15, family = "sans", face = "bold"),
axis.title.x = element_text(size=15, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "none",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "white"),
plot.background = element_rect(fill = "white", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm")) +
scale_y_continuous(limits = c(0, 800), expand = c(0,2))+
scale_x_continuous(limits = c(2010, 2021), expand = c(0,0.2),
breaks = c(2010,2012,2015,2017,2020),
labels = c(2010,2012,2015,2017,2020))
ggsave(hwi_trend, filename = "figures/supplementary/hwi_trend.png", width = 7, height = 5, units = "in", dpi = 600, background = "white")## Warning: Failed to fit group 6.
## Caused by error in `smooth.construct.tp.smooth.spec()`:
## ! A term has fewer unique covariate combinations than specified maximum degrees of freedom## Warning: Failed to fit group 9.
## Caused by error in `smooth.construct.tp.smooth.spec()`:
## ! A term has fewer unique covariate combinations than specified maximum degrees of freedom## Warning: Failed to fit group 14.
## Caused by error in `smooth.construct.tp.smooth.spec()`:
## ! A term has fewer unique covariate combinations than specified maximum degrees of freedom## Warning: Failed to fit group 18.
## Caused by error in `smooth.construct.tp.smooth.spec()`:
## ! A term has fewer unique covariate combinations than specified maximum degrees of freedom# monthly HWI with monthly mean NDVI
monthly_hwi_mean_ndvi <-
ggplot() +
geom_point(data = hwi_ndvi, aes(x = ndvi_monthly_mean, y = HWI, col = park)) +
xlab("Monthly Mean NDVI") +
ylab("monthly HWI") +
scale_colour_manual(name="Park",
values = manual_colors) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "white"),
plot.background = element_rect(fill = "white", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggsave(monthly_hwi_mean_ndvi, filename = "figures/supplementary/hwi_and_ndvi_trend.png", width = 7, height = 5, units = "in", dpi = 600, background = "white")
# NDVI changes over 21 years
ndvi2000_2021 <-
ggplot() +
geom_point(data = all_ndvi, aes(x = year, y = ndvi_monthly_mean, col = park), alpha = 0.1) +
geom_smooth(data = all_ndvi, aes(x = year, y = ndvi_monthly_mean, col = park),method = "gam", se = FALSE) +
xlab("Time") +
ylab("Monthly Mean NDVI") +
scale_colour_manual(name="Park",
values = manual_colors) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=12, family = "sans", face = "bold"),
axis.title.x = element_text(size=12, family = "sans", face = "bold"),
axis.text.y = element_text(size=10, family = "sans"),
axis.text.x = element_text(size=10, family = "sans"),
legend.position = "right",
legend.title = element_text(face = "bold"),
legend.background = element_blank(),
panel.background = element_rect(fill = "white"),
plot.background = element_rect(fill = "white", color = NA),
plot.margin = unit(c(0.2,0.1,0.2,0.2), "cm"))
ggsave(ndvi2000_2021, filename = "figures/supplementary/ndvi_trend.png", width = 7, height = 5, units = "in", dpi = 600, background = "white")## `geom_smooth()` using formula = 'y ~ s(x, bs = "cs")'We fitted a GAM with a negative binomial distribution and a log link function to describe the relationship between the monthly HWIs and the NDVI residuals between 2010-2021 in each park.
# gam for HWI and NDVI residuals ----
hwi_ndvi <- readRDS("C:/Users/grace/Documents/GitHub/HWI_NDVI_parks/data/hwi_ndvi.rds")
hwi_ndvi$park <- as.factor(hwi_ndvi$park)
all_parks_model <- gam(HWI ~
# global smooths
s(residuals, park, bs = "fs", k = 6), #month effect
#weights = Weights,
family = nb(link = 'log'),
data = hwi_ndvi,
method = "REML")
saveRDS(all_parks_model,file ="data/models/all_parks_model.rds")
save(all_parks_model, file = "data/models/all_parks_model.rda")summary(all_parks_model)##
## Family: Negative Binomial(1.012)
## Link function: log
##
## Formula:
## HWI ~ s(residuals, park, bs = "fs", k = 6)
##
## Parametric coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.790 0.254 7.047 1.82e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df Chi.sq p-value
## s(residuals,park) 43.51 133 2299 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.306 Deviance explained = 66.1%
## -REML = 4799.4 Scale est. = 1 n = 1297# plot to colour code model results by park ----
# extract the data
parks = smooth_estimates(all_parks_model, select = "s(residuals,park)") #extract the data
# add confidence intervals
parks = add_confint(parks)
# rename a value, but not necessary
parks$smooth = 'park'
# plot the results ----
gam_plot <-
ggplot(parks, aes(x = residuals)) +
geom_vline(aes(xintercept = 0), col = "grey70", linetype = "dashed") +
geom_line(data = parks, aes(x = residuals, y = .estimate, color = park), linewidth = 0.5) +
# set the colors
scale_color_manual(name = "Park", values = manual_colors) + # c("#333BFF", "#CC6600", "#9633FF")) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.title.y = element_text(size=15, family = "sans", face = "bold"),
axis.title.x = element_text(size=15, family = "sans", face = "bold"),
axis.text.y = element_text(size=8, family = "sans"),
axis.text.x = element_text(size=8, family = "sans"),
legend.text = element_text(size=8, family = "sans"),
legend.title = element_text(size=8, family = "sans"),
legend.key.size = unit(0.35, 'cm'),
legend.key.height = unit(0.35, 'cm'),
plot.title = element_text(hjust = -0.05, size = 10, family = "sans"),
plot.tag = element_text(size=18, family = "sans"),
legend.position = "none") +
scale_y_continuous(limits = c(-2, 3.5), expand = c(0,0.01))+
scale_x_continuous(limits = c(-2, 2), expand = c(0,0.01),
breaks = c(-2, 0, 2),
labels = c(-2, 0, 2))+
labs(x = "NDVI Residuals", y = "log(monthly HWIs)") #tag = 'a)')
ggsave(gam_plot, filename = "figures/park_hwi_ndvi_trends/gam_plot.png", width = 6, height = 5, units = "in", dpi = 600)## Warning: Removed 925 rows containing missing values or values outside the scale range
## (`geom_line()`).Using the results of this model, we visualized the HWI predictions in response to NDVI residuals in each of the 25 parks with their confidence intervals to look for trends in monthly HWIs according to changing park productivity. We then calculated the inflection points in the response of each park to determine their respective NDVI residual with the most monthly HWIs.
PARKS <- c("WATE", "ELKI", "JASP", "WOOD",
"BANF", "YOHO", "KOOT", "REVE",
"PRIM", "GLAC", "WAPU", "FUND",
"KOUC", "NOVA", "KEJI", "AULA",
"NAHA", "FIVE", "PELE", "GBIS",
"THIS", "PEIS", "FORI", "PALB", "IVVA")
RESIDUALS <- seq(-2, 2, 0.01)
RESULTS3 <- list()
max <- list()
for(i in 1:length(PARKS)){
all_parks_predict <- predict(all_parks_model, newdata = data.frame(residuals = RESIDUALS,
park = PARKS[i]),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
RESULTS3[[i]] <- data.frame(park = PARKS[i],
residual = RESIDUALS,
prediction = all_parks_predict$fit,
SE = all_parks_predict$se.fit)
# find inflection point (max)
max_index <- which(RESULTS3[[i]]$prediction == max(RESULTS3[[i]]$prediction))
max[[i]] <- RESULTS3[[i]][max_index, ]
}
RESULTS3 <- do.call(rbind, RESULTS3)
max <- do.call(rbind, max)
saveRDS(RESULTS3, file = "data/models/model_results/RESULTS3")
saveRDS(max, file = "data/models/model_results/max")# plotting the model results for each individual park
# AULA ----
AULApredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "AULA"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = AULApredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = AULApredict$fit + 1.96*AULApredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = AULApredict$fit - 1.96*AULApredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "AULA"),])
# find inflection point (max)
which(AULApredict$fit == max(AULApredict$fit)) #401, 401## 401
## 401# FUND ----
FUNDpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "FUND"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = FUNDpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = FUNDpredict$fit + 1.96*FUNDpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = FUNDpredict$fit - 1.96*FUNDpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "FUND"),])
# find inflection point (max)
which(FUNDpredict$fit == max(FUNDpredict$fit)) #401, 401## 401
## 401# KEJI ----
RESIDUALS <- seq(-2, 2, 0.01)
KEJIpredict <- predict(all_parks_model, newdata = data.frame(residuals = RESIDUALS,
park = "KEJI"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = KEJIpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = KEJIpredict$fit + 1.96*KEJIpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = KEJIpredict$fit - 1.96*KEJIpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "KEJI"),])
# find inflection point (max)
which(KEJIpredict$fit == max(KEJIpredict$fit)) #401, 401## 401
## 401# PALB ----
PALBpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "PALB"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = PALBpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = PALBpredict$fit + 1.96*PALBpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = PALBpredict$fit - 1.96*PALBpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "PALB"),])
# find inflection point (max)
which(PALBpredict$fit == max(PALBpredict$fit)) #189, 189## 189
## 189# THIS ----
THISpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "THIS"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = THISpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = THISpredict$fit + 1.96*THISpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = THISpredict$fit - 1.96*THISpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "THIS"),])
# find inflection point (max)
which(THISpredict$fit == max(THISpredict$fit)) #401, 401## 401
## 401# BANF ----
BANFpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "BANF"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
png(file = "figures/case_study_banff/BANFF_final.png", width = 6, height = 4, units = "in", res = 600)
# make axis title bigger
par(cex.lab = 1.2)
# plot the line for the park
plot(y = BANFpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250), xlab = "NDVI Residuals", ylab = "Monthly HWIs", col = "#EF0096", font.lab = 2)
# upper conf interval
lines(y = BANFpredict$fit + 1.96*BANFpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = BANFpredict$fit - 1.96*BANFpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[hwi_ndvi$park == "BANF",], pch = 16, col = alpha("#EF0096",0.3))
# find inflection point (max)
which(BANFpredict$fit == max(BANFpredict$fit)) #154, 154## 154
## 154dev.off()## png
## 2# GBIS ----
GBISpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "GBIS"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = GBISpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = GBISpredict$fit + 1.96*GBISpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = GBISpredict$fit - 1.96*GBISpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "GBIS"),])
# find inflection point (max)
which(GBISpredict$fit == max(GBISpredict$fit)) #1, 1## 1
## 1# KOOT ----
KOOTpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "KOOT"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = KOOTpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = KOOTpredict$fit + 1.96*KOOTpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = KOOTpredict$fit - 1.96*KOOTpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "KOOT"),])
# find inflection point (max)
which(KOOTpredict$fit == max(KOOTpredict$fit)) #1, 1## 1
## 1# PEIS ----
PEISpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "PEIS"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = PEISpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = PEISpredict$fit + 1.96*PEISpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = PEISpredict$fit - 1.96*PEISpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "PEIS"),])
# find inflection point (max)
which(PEISpredict$fit == max(PEISpredict$fit)) #266, 266## 266
## 266# WAPU ----
WAPUpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "WAPU"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = WAPUpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = WAPUpredict$fit + 1.96*WAPUpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = WAPUpredict$fit - 1.96*WAPUpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "WAPU"),])
# find inflection point (max)
which(WAPUpredict$fit == max(WAPUpredict$fit)) #401, 401## 401
## 401# ELKI ----
ELKIpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "ELKI"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = ELKIpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = ELKIpredict$fit + 1.96*ELKIpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = ELKIpredict$fit - 1.96*ELKIpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "ELKI"),])
# find inflection point (max)
which(ELKIpredict$fit == max(ELKIpredict$fit)) #278, 278## 278
## 278# GLAC ----
GLACpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "GLAC"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = GLACpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = GLACpredict$fit + 1.96*GLACpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = GLACpredict$fit - 1.96*GLACpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "GLAC"),])
# find inflection point (max)
which(GLACpredict$fit == max(GLACpredict$fit)) #401, 401## 401
## 401# KOUC ----
KOUCpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "KOUC"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = KOUCpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = KOUCpredict$fit + 1.96*KOUCpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = KOUCpredict$fit - 1.96*KOUCpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "KOUC"),])
# find inflection point (max)
which(KOUCpredict$fit == max(KOUCpredict$fit)) #401, 401## 401
## 401# PELE ----
PELEpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "PELE"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = PELEpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = PELEpredict$fit + 1.96*PELEpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = PELEpredict$fit - 1.96*PELEpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "PELE"),])
# find inflection point (max)
which(PELEpredict$fit == max(PELEpredict$fit)) #401, 401## 401
## 401# WATE ----
WATEpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "WATE"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = WATEpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = WATEpredict$fit + 1.96*WATEpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = WATEpredict$fit - 1.96*WATEpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "WATE"),])
# find inflection point (max)
which(WATEpredict$fit == max(WATEpredict$fit)) #401, 401## 401
## 401# FIVE ----
FIVEpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "FIVE"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = FIVEpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = FIVEpredict$fit + 1.96*FIVEpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = FIVEpredict$fit - 1.96*FIVEpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "FIVE"),])
# find inflection point (max)
which(FIVEpredict$fit == max(FIVEpredict$fit)) #294, 294## 294
## 294# IVVA ----
IVVApredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "IVVA"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = IVVApredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = IVVApredict$fit + 1.96*IVVApredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = IVVApredict$fit - 1.96*IVVApredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "IVVA"),])
# find inflection point (max)
which(IVVApredict$fit == max(IVVApredict$fit)) #401, 401## 401
## 401# NAHA ----
NAHApredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "NAHA"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = NAHApredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = NAHApredict$fit + 1.96*NAHApredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = NAHApredict$fit - 1.96*NAHApredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "NAHA"),])
# find inflection point (max)
which(NAHApredict$fit == max(NAHApredict$fit)) #401, 401## 401
## 401# PRIM ----
PRIMpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "PRIM"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = PRIMpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = PRIMpredict$fit + 1.96*PRIMpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = PRIMpredict$fit - 1.96*PRIMpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "PRIM"),])
# find inflection point (max)
which(PRIMpredict$fit == max(PRIMpredict$fit)) #401, 401## 401
## 401# WOOD ----
WOODpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "WOOD"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = WOODpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = WOODpredict$fit + 1.96*WOODpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = WOODpredict$fit - 1.96*WOODpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "WOOD"),])
# find inflection point (max)
which(WOODpredict$fit == max(WOODpredict$fit)) #66, 66## 66
## 66# FORI ----
FORIpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "FORI"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = FORIpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = FORIpredict$fit + 1.96*FORIpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = FORIpredict$fit - 1.96*FORIpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "FORI"),])
# find inflection point (max)
which(FORIpredict$fit == max(FORIpredict$fit)) #401, 401## 401
## 401# JASP ----
JASPpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "JASP"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = JASPpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = JASPpredict$fit + 1.96*JASPpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = JASPpredict$fit - 1.96*JASPpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "JASP"),])
# find inflection point (max)
which(JASPpredict$fit == max(JASPpredict$fit)) #165, 165## 165
## 165# NOVA ----
NOVApredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "NOVA"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = NOVApredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = NOVApredict$fit + 1.96*NOVApredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = NOVApredict$fit - 1.96*NOVApredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "NOVA"),])
# find inflection point (max)
which(NOVApredict$fit == max(NOVApredict$fit)) #401, 401## 401
## 401# REVE ----
REVEpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "REVE"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = REVEpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = REVEpredict$fit + 1.96*REVEpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = REVEpredict$fit - 1.96*REVEpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "REVE"),])
# find inflection point (max)
which(REVEpredict$fit == max(REVEpredict$fit)) #401, 401## 401
## 401# YOHO ----
YOHOpredict <- predict(all_parks_model, newdata = data.frame(residuals = seq(-2, 2, 0.01),
park = "YOHO"),
type = "response", # to see how HWI responds to NDVI residuals
se = TRUE # standard error = true --> for looking at confidence interval
)
# plot the line for the park
plot(y = YOHOpredict$fit, x = seq(-2, 2, 0.01), type = "l", ylim = c(0,250))
# upper conf interval
lines(y = YOHOpredict$fit + 1.96*YOHOpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# lower conf interval
lines(y = YOHOpredict$fit - 1.96*YOHOpredict$se.fit, x = seq(-2, 2, 0.01), type = "l", col = "grey60")
# adding the real data into the plots of predictions
points(HWI ~residuals, data = hwi_ndvi[which(hwi_ndvi$park == "YOHO"),])
# find inflection point (max)
which(YOHOpredict$fit == max(YOHOpredict$fit)) #401, 401## 401
## 401